Penney, 44, left Darlington on Thursday after ending his two-and-a-half year reign at the north-east club which is currently in administration.
The Latics moved swiftly to land Penney after the interim manager Joe Royle revealed he would not be staying on at the helm of the club beyond the end of the season.
Penney, who had led Darlington to the automatic promotion places in League Two before their financial difficulties, will officially take over following Saturday's final game of the season at Walsall.
"We are delighted to be able to welcome a manager of Dave's calibre to Boundary Park," managing director Simon Corney told the club's official website.
"He is a very professional and thorough person who ticked all the boxes and who has an excellent track record."