The Lithuanian only left Hearts in February for Norwegian side Viking Stavanger, but accepted a move to Rangers last month.
He has now completed his switch to the Gers and boss Walter Smith is weighing up when to involve the 29-year-old in his pre-season plans.
"We will see how he is," Smith told the club's official website.
"He didn't play in the last couple of games for Viking, but that might be that they were making sure he didn't suffer any knocks before coming to join us.
"We will let him get involved in training this week and then make a decision on whether we use him in the remaining matches."