The Samoan born Leapai replaces American Eric Molina for the fight in Rhode Island
Molina pulled out amidst a dispute his promoter Don King had with the fight terms.
The two will fight on June 29 in the first of Parker's three fight deal with British promoter Eddie Hearn.
The Lauli'i born 39-year-old boxer, who is fighting out of Australia, has won 32 fights of his 43 fights, 25 by knockout.
Parker is fighting for the first time with Matchroom Boxing, the same promotion team that recently dethroned champion Anthony Joshua belongs to.