He returns from Scotland 7s duty in New Zealand following his agreed loan from Edinburgh Rugby and will be available for this Sunday's game against Connacht at Scotstoun Stadium.
The 25-year-old 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 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.”