Mr. Manafort, who has not been accused of any crimes — and who denies any wrongdoing in his political, business and investment dealings — is nonetheless a central figure in the investigation into the interactions of Trump campaign officials with foreign governments. How he got to know Mr. Trump, and how he rose from overseeing the candidate’s operations at the Republican convention to the entire campaign, is very likely to be a focus during coming Senate hearings about possible collusion between the Trump campaign and the Russian government.

“Donald Trump and I had some business in the 1980s but we had no relationship until the Trump campaign called me,” Mr. Manafort, who did not dispute the substance of the documents, wrote in an email forwarded by a spokesman. “A role at the convention was all I was ever interested in; the fact that this role expanded was quite unexpected.”

But it was Mr. Manafort who initiated the process for getting a job on the campaign, the documents show. It began when he sent two succinct memos to Mr. Trump through Thomas J. Barrack Jr., a mutual friend.

A couple of weeks earlier, Mr. Barrack met with Mr. Manafort for “coffee and snacks” at the Montage hotel in Beverly Hills, according to Jason Maloni, Mr. Manafort’s spokesman. He added that Mr. Barrack wanted his old friend to help the struggling campaign deal with potential challenges at the convention.

Mr. Maloni said that the memos were intended only to be talking points for Mr. Barrack’s pitch to the Trump family, but that after reading the packet, the candidate requested a one-on-one meeting with Mr. Manafort.