Albert made 12 appearances for Rovers last season and played in their Betfred Championship Grand Final defeat at Toronto Wolfpack.
He initially joined Leeds in March, after leaving Widnes Vikings and played six times for Rhinos in 2019.
He has been allocated Rhinos' number 35 jersey for next year and returned to training with Leeds, following international duty, at the start of this week.
Albert will join Rovers' first team squad on the January 3 in time for their pre-season fixture against York City Knights two days later.
Rovers' football manager Steve Gill said: "We have been working closely with Leeds Rhinos with a view to bringing Wellington back to the club for the 2020 season and thankfully Leeds have allowed him to re-join us.
"Wellington gave us real presence last season with his strong carries and off-loads and he became a real fans' favourite in his short time he was here.
"Wellington welcomed the opportunity to return to the Rovers, I believe he will give us some extra fire power to an already formidable pack."