The school will seek a waiver for Johnson to be eligible to play in 2014-15, according to the source.
Johnson's commitment to Memphis was reported earlier Wednesday by CBS Sports.
Kevin Stallings said last week that he barred Johnson from returning this season after he failed to meet a "high level of responsibility" that the Vanderbilt coach said he demanded from his players. Johnson, who averaged 13.5 points and 3.6 assists during the 2012-13 season, missed last season after violating university policy.
The addition of Johnson is a boost for a young Memphis squad that lost Joe Jackson and multiple veterans from last season's team.
Memphis coach Josh Pastner needs help in the backcourt and clearly is not above taking a risk on Johnson, the second player who comes to Memphis with red flags.
A few weeks ago, Calvin Godfrey, a big man who attended Southern last season, announced that he will also compete for Memphis next season. Memphis will be Godfrey's fifth school.