Barton has joined Scottish giants Rangers on a free transfer after leaving Premier League-bound Burnley.
Redknapp worked with the former Newcastle United and Manchester City midfielder at Queens Park Rangers, and he has backed the 33-year-old to be an asset to Mark Warburton’s side.
"He's got a real good understanding of football and his role in the game,” Redknapp told BBC Sport. “You give him a job to do and he'll do the job.
"He was as good as anybody defending corners. The amount of balls he headed out the box when I had him, he did his job in the right position that you put him in.
"He'll be a good player for Rangers, I'm sure he will. I'm sure [manager] Mark Warburton will get the best out of him."
Meanwhile, former Rangers star Derek Johnstone believes that Barton should not be judged based on his past.
“A lot of non-Rangers fans are saying he will cause trouble and he will get sent off,” Johnstone wrote about Barton in The Glasgow Evening Times. “Well, time will tell.
“As he said himself this week, he didn’t pick up a suspension in the Championship last season and he seems to have changed his ways after the host of issues he has had in the past.”
Barton may be 33 years of age, but he remains a very good footballer and should be a success at Rangers.
The Englishman was one of the best players for Burnley this past season, as he helped the Clarets get automatic promotion to the Premier League.
The former Newcastle midfielder scored three goals and created 29 chances in 38 league appearances for Burnley.
Barton had a pass accuracy of 75% and a shot accuracy of 31%, and won 67 headers, 15 dribbles and 82 tackles.
Rangers won the Scottish Championship title with ease this past season and will feature in the Scottish Premiership during the 2016-17 campaign.