Wilson will be introduced as coach at a news conference at 4 p.m. ET in Bloomington, a school source told ESPN.com's Adam Rittenberg.
The Associated Press earlier reported that Wilson would be Indiana's next coach, citing a person with knowledge of the search.
Wilson will become the Hoosiers' sixth coach since 1996, and the move comes less than two weeks after athletic director Fred Glass fired Bill Lynch.
Lynch posted losing records in each of his past three seasons in Bloomington and won only three Big Ten games during the same three-year span after leading Indiana to a bowl game in 2007, Indiana's first postseason appearance since 1993.
According to reports in Oklahoma, Wilson told reporters there that he interviewed in Indianapolis on Monday but was not immediately offered the job. After returning to Oklahoma, he was offered the job.
Terms were not immediately available, but Wilson just received a pay raise to $430,000 per year in October.
Some Indiana players and former players were already tweeting about the decision Monday night.
"So i guess we got a new coach. Time to get back to work," offensive lineman Justin Pagan wrote.
Former running back Bryan Payton tweeted: "Ive always been impressed with OU's off."
When Glass fired Lynch Nov. 28, he said the university would be willing to pay top dollar to find a new coach -- thanks in part to the millions each conference school is getting from the Big Ten Network.
Wilson has been at Oklahoma, working with coach Bob Stoops, since 2002. He took over as the sole offensive coordinator in 2006, when Chuck Long became coach at San Diego State.
In 2008, Wilson won the Broyles Award as the nation's top assistant after the Sooners scored an NCAA-record 716 points. Quarterback Sam Bradford also won the Heisman Trophy that season.
This season, the Sooners finished fourth in the nation in yards passing per game (336.8) and were No. 17 in scoring offense (36.4 points).
Wilson might not have the depth of Oklahoma's roster when he arrives, but he could have a talented group to build around at Indiana if everybody stays -- as players said they would.
Wilson will start the rebuilding process with a large group of talented receivers.
Damarlo Belcher, a 6-foot-5, 215-pound junior, returns after catching a team-high 78 passes for 832 yards and four touchdowns. Also back are 6-3, 200-pound receiver Duwyce Wilson, who had 32 catches for 488 yards and three scores, and tight end Ted Bolser, who had five TD catches. Both are redshirt freshmen.
Indiana's most talented runner, sophomore Darius Willis, should be healthy, too. He missed the final eight games after having season-ending knee surgery in October.
Plus, if junior Tandon Doss decides to stay in college instead of leaving for the NFL, Wilson can build around the Hoosiers' most versatile offensive player. The 6-3, 195-pound junior was third on the team in receiving (63 receptions, 706 yards, seven TDs) and rushing (11 carries, 163 yards, one TD).
But he will have to pick a quarterback. Two-year starter Ben Chappell has graduated, and it could be a two-man race between redshirt freshman Dusty Kiel, the nephew of former Notre Dame quarterback Blair Kiel, and redshirt freshman Edward Wright-Baker, who is more of a dual threat.
And Wilson will get to rebuild his personal rivalry with Nebraska, which will become the newest Big Ten member next season. Following Saturday's Big 12 championship game, Wilson talked about the end of the Oklahoma-Nebraska rivalry and compared it to that of the Celtics-Lakers.
Information from The Associated Press was used in this report.