The two clubs had agreed a fee of around £200,000 for Mckay to move to Tannadice on a permanent deal.
However, Mckay, 26, failed to reach a severance agreement with the Lancashire club.
The Northern Ireland international had also been courted by Ross County and Hibernian.
He moved to England in January from Inverness Caledonian Thistle in a deal worth £150,000 but has struggled to make the breakthrough at Wigan, featuring only 10 times for the first team without scoring.
Sixty-two of Mckay's 79 career goals have been scored in Scotland with Inverness. He previously played for Hinckley United and Northampton Town.
Dundee United have signed striker Billy Mckay on a season-long loan from English League One side Wigan Athletic.