Washington (CNN) President Donald Trump and Boeing have struck a deal over the development of two new Air Force One planes at a price tag of $3.9 billion, the White House and Boeing said Tuesday, and the President has asked for the planes to be ready by 2021.

Trump met with Boeing executives last Tuesday in the White House to finalize the deal.

Two officials said the President asked for the new plane to be done by 2021, the beginning of what would be a second term, which is three years sooner than the original plan of 2024. The two 747s are in California now, an official said, and Boeing will be done upgrading the planes by then, but the Air Force testing requirements could take an additional three years.

"He wants to fly on that new plane," a person familiar with the meeting said.

For months, the President has been fixated on a new plane and has repeatedly told his aides that he wants the plane to be completed for his second term. It's an open question whether that can happen -- given a lengthy Air Force testing time.

The White House is touting this as a saving of more than $1 billion from the original estimate of $5 billion.

"President Trump has reached an informal deal with Boeing on a fixed price contract for the new Air Force One Program," White House spokesman Hogan Gidley told CNN. "Thanks to the President's negotiations, the contract will save the taxpayers more than $1.4 billion."

But the cost savings aren't entirely clear.

Trump -- shortly after winning the presidency in 2016 -- tweeted that the planes would cost $4 billion, not $5 billion.

A Boeing official said the price includes work to develop and build two presidential aircraft, including features unique to Air Force One such as a communications suite, internal and external stairs, large galleys and other equipment, as well as structural changes designed to protect and sustain the President and those on board for an extended period of time.

A rendering of the proposed Air Force One, provided by Boeing.

"Boeing is proud to build the next generation of Air Force One, providing American presidents with a flying White House at outstanding value to taxpayers," the Boeing company said in a statement Tuesday. "President Trump negotiated a good deal on behalf of the American people."

This includes some work already on contract, such as development and design work and two 747-8s. It also includes the engineering, manufacturing and development contract, which has not yet been awarded.

A White House official told CNN that the $3.9 billion deal would save taxpayers around $1.4 billion from the original estimate of over $5 billion for the two new planes.

"Boeing is building a brand new 747 Air Force One for future presidents, but costs are out of control, more than $4 billion," Trump wrote. "Cancel order!"

Boeing is building a brand new 747 Air Force One for future presidents, but costs are out of control, more than $4 billion. Cancel order! — Donald J. Trump (@realDonaldTrump) December 6, 2016

Before the tweet, Trump told reporters that the cost of Air Force One were "ridiculous."

"I think Boeing is doing a little bit of a number," Trump said. "We want Boeing to make a lot of money, but not that much money."

The White House is touting this $3.9 billion deal as providing savings of more than $1 billion, an example of Trump's deal-making skills. But the fine print shows a more complicated story. The new Air Force One project was estimated at $4 billion in December 2016. Now, the White House and Boeing said that information was wrong, and it was actually $5 billion.

Boeing CEO Dennis Muilenburg and Trump talked the day after Trump's tweet and the CEO promised that the company would work to limit the cost of the new planes.

"Muilenburg congratulated Mr. Trump on his election win and committed to working with the new administration to control costs as they establish requirements for the new Air Force One to keep the program as affordable as possible and deliver the best value to American taxpayers," said Boeing's statement in December 2016.

More than a year after Trump famously tweeted "Cancel Order" the President and Muilenburg hammered out the new deal during a White House meeting last Tuesday.

The meeting, which was not on the President's daily schedule, came after nearly a year of lower-level meetings between Pentagon procurement officials and Boeing executives that, at times, reached deadlock.

The President, who has repeatedly expressed his exasperation at his aging aircraft, wanted to meet face-to-face with Muilenburg to reach the deal, two officials said. It was seen as rather unusual for the President to be directly involved in negotiations.

The President repeatedly asked in the meeting how soon the plane could be ready, two officials said, and was fixated on a time frame of at least 2021. It remains an open question whether the Air Force can complete its testing and modifications by then. It wasn't scheduled to be ready until at least 2024.

At issue was the price tag for the two 747 jumbo airplanes that the Air Force bought from Boeing last summer. The cost question concerned the modification process -- the conversion of normal jetliners into Air Force One.

"Cost estimates have always been over $5 billion," a White House official said today, adding the President-elect was operating off of "bad information in 2016."

The White House official said the new deal with Boeing would be "managed through over and above contract line items that will be negotiated concurrently with this final contract. The contract ensures quality and safety will not be compromised."

It has long been essential for Boeing to keep up a good relationship with the federal government. The company is a major defense contractor with about $26 billion worth of sales from US government contracts in 2015, which amounted to 27% of its annual revenue.

The current Air Force One planes began service in 1990 under former President George H.W. Bush and they are reaching near the end of their planned life.