The two clubs reached an agreement last month for Doni to join the Reds on a free transfer, with the 31-year-old expected to sign a two-year contract.
"Everything is okay with Liverpool," Doni's agent Ovidio Colucci told asromanews.it. "We are returning to Rome to sign the final documents.
"The deal will be finally completed tomorrow and Doni will be back at Liverpool on Sunday to be available for [Liverpool manager Kenny] Dalglish."
Doni moved to Roma in 2005 from Juventude and is under contract at the Serie A outfit until 2013.
He has been understudy to Julio Sergio in recent seasons, but made 16 league appearances for Roma last term.