Cheesman, a three times Oxford Blue, joined the Championship side in 2012 and has made over 100 appearances.
Club captain Morgan has amassed over 200 games since joining from Newbury in 2008, and has earned representative honours for the Barbarians.
Forwards coach Alan Paver said: "Alex is one of the best back-rowers in the Championship, and Morgs is a legend."
The Pirates have already agreed new deals with prop Marlen Walker and back row Dan Lee whilst another prop, Tyler Gendall, has gone on loan to Harlequins until the end of the season.
Gendall, 22, made his Quins debut in the win at Worcester in the Anglo-Welsh Cup.
The Cornish Pirates are seventh in the Championship and two points off the play-off places ahead of Sunday's home game against London Scottish.
Forwards Chris Morgan and Alex Cheesman have signed new two-year contracts at the Cornish Pirates.