Jones has four caps for Scotland and has played 57 times for Edinburgh Rugby.
He has been a regular for Scotland 7s in the last year and has scored 34 tries in 14 tournaments in the IRB Sevens World Series.
Glasgow Warriors head coach Gregor Townsend said: "We have a number of players away with Scotland and a few injuries in our backline, so Lee joining us is very welcome news.
"I'd like to thank Edinburgh Rugby and Scotland 7s for loaning Lee to us and he will be a quality addition.
"Lee is in great physical shape and has been in try-scoring form for Scotland 7s. I know him well from my time coaching with Scotland and he will fit in well at Scotstoun.
"He will be joining us tomorrow from the Scotland 7s camp in New Zealand, so we expect him to be available for this weekend's game against Connacht."
Scotland 7s head coach Stephen Gemmell said: "Lee has been given an opportunity to have game time in the RaboDirect PRO12 which is great for him as a player and although disappointing to lose him, we are fortunate enough to call on Darren Gillespie who has been living in New Zealand in Christchurch and therefore able to join up with the squad."
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