A 6'8" forward, the 28-year-old also featured for Northampton Saints before switching to the Ricoh Arena, playing 93 games across six seasons before his move to the Guinness PRO12.
"James has been part of a competitive mix of second row players at Wasps but has shown his talent when given the chance," said Lam.
"He brings a vast amount of experience from playing in both the Aviva Premiership and European Champions Cup and will greatly boost our second-row options. We're all looking forward to welcoming him to Connacht Rugby."
Connacht have had a frustrating start to the defence of their Guinness PRO12 crown, losing their first four games to sit bottom of the table.
But with a debut season in the European Champions Cup to look forward to, Cannon feels it's a good time to be joining the region.
He said: "I'm very excited about the new challenge in Connacht and look forward to working hard to try to get more first team opportunities and to play my part within the squad."