Wallace, 22, had a two-month spell with the Lions last season, scoring one goal in 14 appearances before being recalled by Wolves in March.
His move to The Den is with a view to a permanent move in the summer.
Centre-back Cooper, 21, has scored four goals in 54 appearances since making his debut for Reading in August 2014.
The England Under-20 international has featured five times for the first-team this season, and had two further outings in the EFL Trophy.
The pair are the south London club's first two signings of the January transfer window.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.
League One side Millwall have re-signed Wolves midfielder Jed Wallace and brought in Reading defender Jake Cooper on loan until the end of the season,