The defender played for Boro between 1972 and 1977 and helped the side reach the FA Cup fourth round in the 1974/75 season, by beating Stockport, Halifax and Rotherham before eventually losing to Peterborough in front of more than 31,000 fans at Stoke City's old Victoria Ground.
He was also in the Rangers side that reached the FA Trophy final in 1976, where they lost 3-2 after extra-time to Scarborough at Wembley.
Morris made around 270 appearances in his five years with the club and was known for rarely missing a game during that time.
The former Oxford United and Port Vale footballer, who was originally from East London, died on March 15 aged 77.
Now, Rangers volunteer and long-term fan Phil Bennett has paid tribute to Morris as he remembers an iconic overseas trip.
"We signed him for Port Vale and he was known to be an Oxford United player before, so we know from what he'd done that we'd signed a decent centre-half," the 64-year-old said.
"I think initially he was a centre midfielder at his league clubs but we played him as a centre-half.
"After playing in the 1976 final he came with us to the Anglo-Italian cup.
"It was a competition for Football League clubs but it became notorious for fighting and after cancelling it, it was resurrected as a non-league competition.
"In England they chose two sides from the Northern Premier League, two sides from the Southern League and two sides from the Isthmian League.
"They each played two Italian sides and the top two sides from each country played each other in the final – Mick went to Italy with us.
"Rangers played Monza first and lost 1-0, and in the Italian system, Serie C was classed as non-league and the other side in our group was Udinese – and we beat them 3-2 at home."
After the two games in England, the Boro players travelled to Italy to face Monza and Udinese again – but the results didn't go there way.
"Quite a few Rangers fans went to Italy, we were the only English side to take many fans," Bennett added.
"We'd been there a week and you can imagine what the players were getting up to.
"We turned up to play Udinese and lost 6-2 and the fans weren't happy.
"They trained hard for the second match against Monza and I still reckon it's the best I've ever seen Rangers play, they were tremendous that night, but unfortunately we drew 1-1 to a blatantly offside goal – the player must have been 10 yards offside.
"Monza then qualified as the top Italian side and beat Wimbledon 1-0 in the final."
Despite the disappointment over the trip abroad, Bennett left with many happy memories of that famous Rangers team that Morris was integral to.
What stood out for him about Morris, however, was his quiet and professional demeanour.
"He wasn't a naughty player, I could give you loads of anecdotes about players who treated it as a holiday in Italy, but Mick was the perfect gentleman," Bennett said.
"He was a real gentleman, he wasn't a troublemaker and he was a very competent central defender.
"Players kept themselves to themselves in those days and you tend to remember the troublemakers and he wasn't one of them.
"He did the job and wasn't flamboyant on or off the field – he was an honest man and player."