Tunnicliffe, 24, worked with Wigan boss Warren Joyce when he was coming through the Manchester United youth system.
Browne, 19, made his professional debut in the Europa League this season and has also played in the EFL Trophy.
"Marcus is a young player with great potential and will strengthen our group," said manager Joyce.
"Ryan has got a terrific attitude first and foremost. He has built up considerable experience now in this division and we are confident he can be a really positive influence to the group in the immediate future."
Both players are available for Wigan's Championship game against Brentford on Saturday.
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Wigan Athletic have signed midfielders Ryan Tunnicliffe and Marcus Browne from Fulham and West Ham on loan until the end of the season.