United forked out an initial £75m to sign Lukaku, 24, from Everton.
The Belgium international has emerged as one of the Premier League's most prolific strikers in recent seasons.
His tally of 25 top flight goals last term was bettered only by Tottenham star Harry Kane.
And Cole sees no reason why Lukaku can't continue to find the back of the net on a regular basis for the Red Devils.
"He’s a massive signing," he told MUTV.
"They’re all big-money signings nowadays but he’s proven in the Premier League.
"He’ll get goals and that’s what Manchester United missed last season.
"I think he’s got plenty of those in him.
"Since he left Chelsea earlier on in his career, the way he’s gone about his business is by getting goals.
"He did it at West Brom, then got quite a few more goals at Everton, and hopefully that trend will continue at Manchester United."
