Finney, 37, replaces Perry Clark, who took the coaching job at Miami after 11 years at Tulane.
Finney, a native of Mullens, W.Va., has been an understudy of Kentucky coach Tubby Smith since 1992, when Smith took the head coaching job at Tulsa. Smith was hired at Tulsa by Rick Dickson, who was hired as Tulane's athletic director in December.
Finney arrived at Tulsa in 1991, and Smith kept him as an assistant on the advice of Dickson, who said Finney impressed him right away.
"I've watched Shawn grow and develop over the last 10 years at three outstanding programs to become the premier assistant at the premier program in the country," said Tulane Athletic Director Rick Dickson. "I believe he'll be a huge success for Tulane University."
Finney followed Smith to Georgia and then Kentucky, where he helped guide the Wildcats to a national championship three seasons ago.
Tulane, which was forced to disband its basketball program following a point shaving scandal in the 1980s, revived the program with Clark's assistance. The team has since made several NCAA appearances and went 20-11 last season.
"It is an exciting time to be associated with Tulane," Finney said.
He said his time as a Division I coach, as well his playing experience at the Division III level, will both prove valuable.
"I know what type of athletes you need to win at the highest level," Finney said. "I also know from being at the Division III level what it's like to have high academic standards. I think those two things prepare me for the job at Tulane."
Finney said he would talk with current and recruited players Wednesday and leave Thursday on his first recruiting trip for Tulane. Among those Finney intends to meet with is Trello Galloway, who has indicated he wants to follow Clark to Miami. Galloway, a 6-7 forward, averaged 3.5 rebounds and 3.7 points per game in his freshman season.
Finney said he has several people in mind for staff, but named only Tulane assistant Anthony Anderson, with whom he expected to meet Wednesday. Clark took Tulane assistant Brock Kantrow to Miami with him.
In Kentucky, Smith said he expects his departing assistant to bring to Tulane an up-tempo style of basketball highlighted by three-point shooting and pressure defense.
"He's been the glue to the success I've experienced at Tulsa, Georgiand Kentucky," Smith said. "He's one of the rising stars who has prepared for this day by coming up through the ranks."
As a player, Finney spent two seasons at Garret Community College before finishing his basketball career as a starting guard in his senior season at Fairmont State.
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