The United States international spent four years at Old Trafford before Moyes signed him for the Toffees.
Since Moyes moved in the other direction to replace Sir Alex Ferguson things have not gone as well as expected but Howard is confident, given time, that the 50-year-old will turnaround their current slide.
"I think the club will succeed and David Moyes, given the right time, will be a huge success," he told ESPN FC.
"David Moyes never takes a backward step. He always believes that he can do the right things.
"He believes in his methods, he believes in the players that he brings to a club and that makes for a really good working environment over a long period of time."
Howard thinks part of the problem stems back to when Moyes' first summer of recruitment did not go to plan.
However, he does not believe a failure to attract the required names then will hinder the Red Devils boss in the future even if he cannot offer new signings Champions League football next season and pointed to Wayne Rooney extending his contract as an example.
"Any time you are at club you want your biggest players in order to attract other bigger players and they have done that so I am certain they will have a pretty good summer spending money," Howard added.
"The teams around them, over the summer, brought in five, six, seven players of quality, spent near £100 million and for whatever reason Manchester United only brought in one player who we know well, (former Everton midfielder) Marouane Fellaini, but has been often injured this season so if you do the math, that doesn't bode well."