The 26-year-old has been in hot water with the club after missing the first week of pre-season training.
He also returned late to Swallows after doing duty at the Africa Cup of Nations in Angola in February.
Mbesuma has failed to impress since joining the Birds from Mamelodi Sundowns last year and his departure had seemed imminent for some time.
A club insider told this website: “The club and the player have parted ways.
“It was an agreed decision from both parties.
“Him returning late from training and also the issue of his performances was a huge disappointment to the club last season.”
The former Kaizer Chiefs, Portsmouth, Bursaspor and Sundowns frontman has a long history of poor time-keeping.