The centre has played 119 times during his nine years with the Warriors and has scored 17 tries.
The 28-year-old made his Scotland debut in 2013 against Samoa and has gone on to represent his country 31 times, crossing the try line seven times in the process.
Dunbar has only played eight times for Glasgow this season and moves to the English Premiership side in search of more regular game time.
The club can recall him from his loan at any time.
Glasgow Warriors Head Coach, Dave Rennie, said: "Alex is a good man and has given everything to the club on and off the pitch for the best part of a decade.
"We have a lot of competition at centre and this is a good opportunity for him to go and play more regularly and test himself in a different competition.
"We wish him and Lois all the best in Newcastle."