Washington (CNN) Pete Buttigieg endorsed Joe Biden for president Monday night, telling a crowd in Dallas the former Vice President is the right candidate to "bring back dignity to the White House."

"When I ran for president we made it clear that the whole idea was about rallying the country together to defeat Donald Trump and to win the era for the values that we share," Buttigieg said at a campaign stop.

"And that was always a goal that was much bigger than me becoming president and it is in the name of that very same goal that I am delighted to endorse and support Joe Biden for President."

The endorsement is a boon for the former vice president, and comes at the same time that Amy Klobuchar is ending her campaign and backing Biden. The Minnesota senator will officially make her endorsement on Monday night in Dallas, too, a campaign aide told CNN.

The endorsements represent a coalescing of the more moderate wing of the Democratic Party around Biden and a rejection of Vermont Sen. Bernie Sanders, who -- after strong showings in Iowa, New Hampshire and Nevada -- represents the most significant challenge for Biden.

Sources told CNN earlier Monday that Buttigieg was weighing whether to endorse Biden after exiting the Democratic presidential race late Sunday night. The two spoke on Sunday night, sources said, and Buttigieg also spoke with former President Barack Obama.

While Buttigieg spent the final weeks of his campaign focused on taking on front-runner Sen. Bernie Sanders, the former mayor did focus his attacks on Biden at different points in the campaign and Biden directed his share of criticism toward Buttigieg, who he was competing against for the moderate wing of the party.

Despite the acrimony, it is common for candidates who once sparred in a primary to come together once one drops out.

That much was made clear Monday night when Biden told supporters that Buttigieg reminds him of his son, Beau, who died of brain cancer in 2015 at the age of 46.

"I don't think I've ever done this before, but (Buttigieg) reminds me of my son, Beau. I know that may not mean much to most people, but to me it's the highest compliment I can give any man or woman," Biden said.

"Like Beau, he has a backbone like a ramrod. I really mean this. I think about it," Biden said.

Buttigieg, the former mayor of South Bend, Indiana, spoke to Biden by phone after delivering his concession speech, two people familiar with the conversation said. Biden congratulated Buttigieg on his campaign and asked for his endorsement. Buttigieg did not make an immediate decision, telling advisers after the call that he wanted to think about it overnight.

Obama praised Buttigieg on his campaign and his decision to leave the race, source said, noting how difficult it is to disappoint supporters and admirers. Obama also told Buttigieg he ran a historic campaign to be proud of.

The former President made clear the decision on whether to endorse a candidate is Buttigieg's alone to make, two people familiar with the call say. The two discussed the leverage that Buttigieg has now -- and how he could be most helpful in shaping the race.

During the campaign, Buttigieg cast Biden as out of step with the current moment in American politics, and when Biden confronted him about these criticisms during a debate in New Hampshire, Buttigieg said the achievements made by the Obama administration "were phenomenally important because they met the moment, but now we have to meet this moment, and this moment is different."

Buttigieg's more direct criticism of Biden came days before the Iowa caucuses, when he responded to Biden suggesting nominating someone "new" would be a risk.

"I hear Vice President Biden saying that this is no time to take a risk on someone new," Buttigieg said in Decorah, Iowa. "But history has shown us that the biggest risk we could take with a very important election coming up is to look to the same Washington playbook and recycle the same arguments -- and expect that to work against a president like Donald Trump."

Biden lobbed his fair share of criticism at Buttigieg, too, including in a scathing, mocking digital ad that diminished Buttigieg's experience as a mayor. When asked about how that criticism is similar to attacks leveled against Obama in 2008, Biden told reporters in New Hampshire, "Oh come on, man. This guy's not a Barack Obama."

The two, however, also shared warm moments on the trail, the most notable being when Buttigieg turned a debate question on attacks President Donald Trump was leveling against Biden and his family into a defense of the former vice president.

"Look, the vice president and I and all of us are competing, but we've got to draw a line here," Buttigieg said. "To be the kind of president, to be the kind of human being, who would seek to turn someone against his own son, who would seek to weaponize a son against his own father, is an unbelievably dishonorable thing."

Buttigieg ended his presidential campaign Sunday night in South Bend after he struggled to compete in South Carolina's primary.

Speaking to supporters Sunday, the former mayor said, "I know that as this campaign ends, there comes disappointment that we won't continue."

"But I hope that everyone who has been part of this in any way knows that the campaign that you have built and the community that you have created is only the beginning of the change that we are going to make together," he said.

CLARIFICATION: This story has been updated to clarify the event in Dallas where Buttigieg endorsed Biden. It was at a campaign stop.

This story has been updated to reflects Buttigieg's endorsement of Biden on Monday night.