The 23-cap Red Rose back has enjoyed an impressive start to the season, in which he has not missed a kick and is seen by some as a dark horse for the Lions.
He will be available to feature in Bath's next two fixtures, against London Irish and Sale, before jetting to France.
Barkley has spent all but one season of his career at Bath but could not resist the lure of Top 14 and Heineken Cup rugby as he enters the twilight of his career.
"I will be forever a Bath boy but this, for me, was simply the opportunity of a lifetime and one I just couldn't ignore," said the 30-year-old.
"I will miss the club always, and I wish all of my mates here the very best. I believe they are a special group with special coaches, and I hope they achieve everything they desire.
"I leave with a heavy heart to take on what will be a big challenge but one that I am going to try and grab with both hands."
Bath have plenty of cover in the position with World Cup winner Stephen Donald close to a return and Sam Vesty able to slot in.
But Bath head coach Gary Gold admits Barkley will be hugely missed at the Rec.
"Barks is a great bloke and a top player," said Gold
"I could not have been more impressed with both his attitude and his incredibly professional approach since I arrived at the club.
"As a senior player, he could not have worked harder or been more welcoming to us as a group of coaches, but every now and then an offer lands on the table that a bloke just can't refuse.
"We are sorry to see him go, but he goes with our blessing. He will always be welcome here."