Fletcher scored the winner for West Brom against Newcastle at The Hawthorns in the Premier League on Monday afternoon.
The 31-year-old Scotland international midfielder found the target in the 78th minute, as the Baggies registered a narrow 1-0 victory and returned to winning ways in the league.
Redknapp, who played for Tottenham and Liverpool among other clubs, was impressed with Fletcher’s performance against Newcastle and has showered praise on him.
“What an important goal that was for Darren Fletcher and West Bromwich,” the former England international midfielder has written in The Daily Mail.
“Tony Pulis’s side had not won since November so they needed to show some character against Newcastle. And nobody does that better than Fletcher.
“After suffering with ulcerative colitis there were questions about how that would affect Fletcher’s life, let alone his career. But he is a fighter and is always desperate to win.
“It’s no surprise he was a go-to man for Sir Alex Ferguson at Man United because he is someone you can rely on. That’s why Pulis took the gamble to sign him — you need real characters in the dressing room if you want to win.”
Fletcher started his professional club football career at Manchester United and played for the Red Devils until the middle of last season.
The Scotsman joined West Brom on a free transfer in February 2015 after leaving United. The 31-year-old has proven to be a superb signing for the Baggies and has been a leader for the team.
Fletcher scored one goal and created 13 chances in 15 Premier League appearances for West Brom last season.
So far this campaign, the former United midfielder has scored one goal and created 12 chances in 19 league matches for the Baggies.