The pair will make an official announcement Thursday at 4:30 p.m. ET.
Both players were considered first-rounders, according to several NBA executives. The 6-foot-10 McGary was terrific in the NCAA tournament after playing sparingly for much of the season. Robinson was also up and down through his freshman campaign, but NBA general managers still love his potential.
"These two are very interested in being leaders," coach John Beilein said at Thursday's press conference. "I sense right now they're growing more and more comfortable in a leadership role."
McGary averaged 7.5 points and 6.3 rebounds this season, playing fewer than 20 minutes per game. During the tournament, though, McGary put up 14.3 points and 10.7 rebounds. Robinson averaged 11.0 points and 5.4 boards.
"We want to get back to that championship game and hopefully win it," Robinson said at the presser.
Michigan lost Trey Burke and Tim Hardaway Jr., early to the NBA, but the Wolverines -- who lost to Louisville in the national title game -- will return McGary, Robinson, Nik Stauskas, veteran big man Jordan Morgan and point guard Spike Albrecht.
"There's still plenty for me to work on and get better," McGary added. "I'm just excited for what lies ahead."
Quotes from the Associated Press were used in this report.