The 18-year-old frontman moves to the Latics on a youth loan until the end of the season, joining fellow Red Sheyi Ojo at the DW Stadium.
"We had a long chat about Jerome and we both feel that this is a positive step for him to make in his career, which will hopefully benefit both clubs," Mackay told the Latics' website.
"We have to thank Liverpool for allowing him to come to Wigan, but they have seen how well Sheyi is progressing and that we are a club who will nurture a young player with potential. We are all hopeful he can make a good contribution during his time here."
Sinclair, who has 22 goals for Liverpool's youth sides this season, will wear the number 31 shirt and could make his debut against Watford tomorrow night.
He has made one senior appearance for Liverpool, coming off the bench in the League Cup against West Bromwich Albion shortly after his 16th birthday on September 26, 2012.