The 27-year-old quit Scotstoun when his contract expired at the end of the season and was widely expected to move to France.
However, the 31-times capped back has opted instead for the Twickenham Stoop.
He becomes the club’s second international recruit this summer after Italy fly-half Tommaso Allan, the former Scotland under-20 international, who will join Quins from Benetton.
Jones said: “To be able to join the reigning Premiership champions and a side that plays such an attractive brand of rugby is a rare opportunity and one that I couldn’t turn down.
“There is a great playing group here and some fantastic coaches, and I can’t wait to get stuck in.”
Quins attack and backs coach Nick Evans added: “Huw made a big impact when he burst onto the scene a few years ago, and he has fantastic instincts for the game.
“Huw is an attack-minded player, and we believe he will fit into the Harlequins way well.
“We look for players who will suit the Harlequins DNA, and we see that in Huw.”
Jones was often deployed as a full-back by Glasgow by prefers to play in the centre and it was in this position that he won a Scotland recall last season.
He played in all five Six Nations matches, starting in the record win over Italy and coming on as a replacement against England, Wales, Ireland and France. He scored tries in the matches with Ireland and Italy.