The 21-year-old had been recalled from his loan spell with Queens Park Rangers on Friday before completing his move to the DW Stadium.
Mlakar arrived at Albion last January on a three-and-a-half-year contract.
He returned to Slovenia on loan in the same window, and scored 15 goals in 36 games to help NK Maribor secure the league title.
He joined QPR in the summer and made eight appearances in all competitions for Mark Warburton’s side. He has also represented Slovenia at under-16, under-17, under-19 and under-21 level.
Technical director Dan Ashworth said: "This is a great opportunity for Jan to go and get some experience at a really competitive level in the Championship. We wish Jan well and we will be monitoring his progress at Wigan during the remainder of the season."