The 30-year-old centre has teamed up with the Aviva Premiership new boys after being without a club since April, having been sacked by Cardiff Blues over his drunken behaviour on a flight returning from a game in Glasgow.
The move is a gamble for the Exiles, who won an appeal to play in the Premiership next season less than two weeks ago.
But Henson previously worked with Jones during his time at the Ospreys, producing arguably the best rugby of his career and helping the region win two Celtic League titles and an Anglo-Welsh Cup.
Jones is confident that he can get the best out of Henson but he has warned plenty of patience will be required given his lack of match action over the last three years.
Jones told Sky Sports: "There's a good chance he'll never reach those heights (of his time at the Ospreys) again to be honest with you, but he just needs to get up to speed and establish himself and I'm not really confident he'll become a very, very good player until about maybe mid-October, November.
"The guy needs a bit of time, he needs a bit of space, his tools are quite blunt and he'll need to sharpen them up, so he's got a lot of work ahead of him that he's prepared to get on with.
"He's rolling his sleeves up, and all you can do is offer people opportunities and it's up to them how they take it but we're confident that he can deliver."
London Welsh are Henson's fifth club in little over 18 months after being released by the Ospreys in 2010 and having short stints at Saracens, Toulon and the Blues.
His spell in France was also been marred by an alcohol-related incident, with the club suspending him for a week after a nightclub altercation with two team-mates.
The Exiles have not disclosed the length of Henson's contract but he will train with his new team-mates on Wednesday.
London Welsh managing director and former Wales flanker John Taylor said: "He is the first to admit things have gone a little haywire over the last few years but he has impressed on me that he still feels he has a lot to prove as a rugby player and is determined to ensure he is not remembered as somebody who never fulfilled his great potential.
"I am confident he will fit in well here and it is obvious he cannot wait to get back to what he does best - playing rugby."
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