Fly-half Clegg joins from Newcastle Falcons after signing a short-term contract for the duration of the Rugby World Cup, subject to medical.
He made 55 appearances for Harlequins over four seasons at Twickenham Stoop and was part of the squad which won the Aviva Premiership title in 2012.
The 25-year-old, who was born in Hannover, has had two stints with Newcastle Falcons - making 50 appearances for the Aviva Premiership side.
He has represented England Saxons and England Under-20s.
Rory Clegg said: "I'm looking forward to moving to Glasgow at the end of the month to start pre-season training.
"This is a great chance for me to join the GUINNESS PRO12 champions and play at high level during the Rugby World Cup.
"It's an exciting time to join the club as they begin the defence of their title."
George Hunter has been at Scotstoun for five years, after coming through the Scottish Rugby Elite Development Programme.
The 23-year-old loosehead has made three appearances for the club and last season played for Ayr in the BT Premiership.
Props Strain and Findlay both played for Glasgow Hawks in the BT Premiership last season.
Strain signed a short-term training contract with the Warriors last September and the 27-year-old former Dalziel player previously represented Newcastle Falcons on 12 occasions.
Findlay, who has also played for Dalziel, made 22 appearances for Glasgow Hawks last season.
The 28-year-old loosehead comes in to further bolster the front-row options for the start of the new campaign, which gets underway at the start of September.
Glasgow Warriors head coach Gregor Townsend said: "We're continuing to work hard to recruit players for the new season and we're delighted to welcome Rory (Clegg), George (Hunter), Gary (Strain) and Steven (Findlay) on board.
"Rory is an experienced midfielder, having played more than 100 games during his time with Harelquins and Newcastle Falcons.
"It's great to be able to add him to our squad for the start of the season.
"He played very well at stand-off at the end of last season for Newcastle and he is a quality fly-half who has the physicality and rugby ability to also play elsewhere in the backline.
"George, Gary and Steven also join us on short-term deals and they will have an opportunity to compete for places in the front-row at the start of the season.
"All three have been training with us over the last few weeks and put in a huge amount of effort, and have shown a number of improvements already. We're expecting further progress when we return for the second block of our pre-season training in the last week of July.
"We're also close to adding further depth to our squad ahead of the new season."
63x46.png){kind=logo}