Morrison was one of two players to join Boro on transfer deadline day – Harold Moukoudi being the other – but the midfielder has so far endured a chequered career.
Once touted as a future star by Sir Alex Ferguson, Morrison has struggled to realise his potential during spells at a host of clubs such as West Ham, Birmingham, Atlas FC and Ostersunds.
He was not signed in time to feature in the 1-1 draw with Blackburn, but will hope to make his debut in next weekend’s Championship game at Brentford.
Woodgate said: “I just think he’s an absolutely outstanding player, and I think we can get the best out of him.
“People say he’s had issues, but who hasn’t had issues? I’ve had a few myself. It doesn’t concern me one little bit.
“He’s a top lad, a really nice kid. Sometimes the press portray you in the wrong way, and I think that’s happened with Ravel.
“Listen, we all mistakes, I’ve done that myself, but he’s a good kid, a good lad. He’ll fit right into the dressing room and I’m really pleased to have him.”
Woodgate watched his Middlesbrough side come from behind to claim a draw with Blackburn, with Hayden Coulson’s first senior goal cancelling out Lewis Travis’s opener for Rovers.
Blackburn chief Tony Mowbray and midfielder Stewart Downing received a warm welcome on their return to the Riverside.
Middlesbrough: Pears, Howson, McNair, Fry, Spence, Wing, Saville (Coulson 71), Johnson, Tavernier (Assombalonga 62), Nmecha (Gestede 84), Fletcher. Unused substitutes: Mejias, Clayton, Wood-Gordon, O’Neill.
Blackburn Rovers: Walton, Nyambe, Lenihan, Adarabioyo, Bell, Travis, Downing (Johnson 82), Gallagher, Holtby (Bennett 37), Rankin-Costello (Graham 67), Armstrong. Unused substitutes: Williams, Samuel, Leutwiler, Brereton.
Referee: M Donohue (Sale).