Wells, a member of the England Under-20s squad that lifted the World Junior Championship title last summer, joins the Championship side after gaining experience with Loughborough Students this season and in the LV= Cup with Tigers.
The Blues have moved to bring in 20-year-old Wells following injury to Ben Gulliver, who spent a brief spell with Tigers a couple of seasons ago.
Bedford director of rugby Mike Rayer said: “We’re delighted to be able to welcome Harry and we really are extremely grateful to Leicester for allowing us to sign him until the end of the season.
“Ben has taken a bit of a knock to his neck and, while we don’t know the full extent of his injury, we thought it appropriate to move swiftly and bring in some extra cover.
“Harry has been working under the tutelage of Richard Blaze at Tigers and is an outstanding prospect who has been rubbing shoulders with the likes of Geoff Parling, Louis Deacon, Graham Kitchener and Ed Slater so hopefully he can make a real impression with us and force his way up the pecking order at Leicester next season.”