Jenkinson, who is currently on loan from Arsenal, knows Song from his time at the Emirates Stadium before the Cameroon international departed for Barcelona.
In a blog for the West Ham website, Jenkinson wrote: "Alex Song made his debut at Hull too and I know him really well from his time at Arsenal. He's a top player and a great asset for this Club.
"He knows what he can do, and people will gradually see that too. He demands time on the ball and he gets it - he's that sort of player and he's that good.
"I think he'll be fantastic this season and it's great to see him playing now because he's in a similar situation to me. He needed to get fit and he's fit now now, so hopefully he has a great season."
Song was linked with several Premier League clubs after it became apparent Barcelona were prepared to let him leave the Nou Camp.
Certainly, an experienced player with such pedigree and a good amount of power is bound to add a lot to the midfield of a side that finished in mid-table in the Premier League last season.
Sides that face West Ham this season know they are going to be face a difficult encounter in the middle of the park, and there will be times when they'll find it difficult to control proceedings with Song's presence.