The head of the Lisbon club's general assembly told reporters late on Monday that Sporting's board elections were scheduled for March 23.
"Sporting's board decided to renounce their mandate," Eduardo Barroso said. "The board will stay in function until the elections and the club's managing bodies plead for fans to support the club during this period."
Godinho's reign was tainted by instability and one of the deepest crises in Sporting's history, with the club lagging in ninth in the league, 26 points behind joint-leaders Porto and Benfica.
Since Godinho took over in March 2011, Sporting have had five different head coaches - Domingos Paciencia, Sa Pinto, Oceano Cruz, Franky Vercauteren and Jesualdo Ferreira - and have failed to live up to the tag of being one of Portugal's "Big three" clubs together with Porto and Benfica.
Sporting last won the league in 2002 and have finished 16, 28 and 36 points behind the champions in the past three seasons.