Haith would not comment on the terms of the deal, but a source with direct knowledge told Andy Katz of ESPN.com that Haith will receive a seven-year deal, which includes a one-year extension after the first year, at an average of $1.85 million.
He will be introduced as the replacement for Danny Manning, who left for Wake Forest earlier this month, on Friday afternoon.
"We had great leadership at Missouri and I had a great relationship with athletic director Mike Alden and our administration,'' Haith told ESPN on Friday morning. "This was a great fit for me and my family.
"The fact that the national champion came out of this league was attractive. This has been a great basketball job at Tulsa with a great tradition with Tubby Smith, Nolan Richardson and most recently with Danny Manning. There is great leadership here at Tulsa and they are showing a great commitment.''
Next season, the Golden Hurricane will join the American Athletic Conference, which includes national champion Connecticut.
Haith said he would take his Missouri staff with him, although he said at least one assistant was still pursuing another job and he wasn't sure if he would follow him to Tulsa.
A surprise hire by Missouri out of Miami three years ago, Haith led the Tigers to the NCAA tournament in two of his three seasons. He had a 76-28 record at Missouri.
Brown, who had transferred to Missouri from Auburn, led the Southeastern Conference with 19.9 points per game last season. Missouri went 7-8 after the start of February and missed the NCAA tournament for the first time in six years.
While Missouri plays in the high-profile SEC, Tulsa might be a more stable situation for Haith.
The Golden Hurricane went 17-16 and played in the CBI tournament two years ago. This past season, Tulsa improved to 21-13, won the Conference USA tournament and reached the NCAA tournament with a young team. Sophomore guard James Woodard was a second-team all-conference pick, and forwards Rashad Smith, Lew Evans and D'Andre Wright and guards Shaquille Harrison and Rashad Ray were sophomores who played significant roles.
Haith served a five-game suspension to open this past season as a result of discipline handed down by the NCAA for failing to promote an atmosphere of compliance while coaching at Miami.
An NCAA investigation found that Haith and an assistant coach had provided former booster Nevin Shapiro $10,000 after he threatened to expose previous improper contact with high school recruits and amateur coaches.
Shapiro initially demanded Haith return a $50,000 donation, but the coach refused. The unidentified assistant then loaned Shapiro $7,000, which he later repaid. The NCAA also found that Haith helped his assistant pay off Shapiro's mother.
Shapiro is a former booster and a convicted felon serving a 20-year sentence for masterminding a $930 million Ponzi scheme.
Haith's suspension was tied to a larger 2½-year NCAA investigation of Miami that also involved the football team.
ESPN.com's Andy Katz and The Associated Press contributed to this report.