Cole has returned to Upton Park on an 18-month deal, nine years after he left his boyhood club for Chelsea.
The 31-year-old has been written off by many after a miserable two-and-a-half year spell at Liverpool.
But Allardyce insists Cole, who won the last of his 56 England caps in 2010, can thrive again with a run of first team games.
“I'm delighted. He's a quality player," the Hammers boss told talkSPORT.
"It's time to take Joe back to his hometown club, where he started, where he realised his dream and give him the opportunity to start playing regular first team football again.
"He's desperate to play first team football again on a regular basis and that is one of the main reasons why we brought him back again. Hopefully, he can produce what we know he can.
"He's got 56 caps for England and is still just in his early 30s. He still has a long career ahead of him and hopefully we can benefit.
"He can play anywhere, wide on the left, on the right, or in the hole behind the front man. We’ll get him doing what he’s best at, getting on the ball to start opening up defences."