Reid told BBC Radio Five Live: "He is one of only three managers in our history to have won the league three times in a row. He has taken a team with very limited resources compared to big Premier League teams to the final 16 of Europe two years running - never before done in our history.
"While we have some weaknesses which we will address, we have unlimited ambition, a tremendous management team, Gordon Strachan is now supplemented by Neil Lennon and of course the late Tommy Burns. I think the best is yet to come for Gordon and his team and I hope he's there."
Reid, who took over as chairman in mid-season, saw Rangers lead the way in the title race until being beaten twice by Celtic in April saw them lose momentum.
Rangers were also faced with a fixtures pile-up, which was the knock-on effect of their success in Europe and both domestic cups, and a 2-0 defeat at Aberdeen on Thursday night ended their hopes of a final-day turnaround.
Reid said: "Rangers had a great difficulty, and that is that success breeds its own challenges, so the further they went in all of their contests, the greater the number of games they had.
"We've come through that in the past, Manchester United for instance found it in the league and Europe as well. But at the end of the day the mark of true champions is endurance, consistency.
"It's not just skill. That's important, but it is the capacity to keep going when things get very difficult.
"That's why I'm particularly delighted for our fans, who stuck by us when we went through a sticky patch, and for Gordon Strachan who was getting attacked, very unfairly, by some of his critics only a few months ago.
"Gordon's team responded in the way my father always told me to respond and that is 'put the ball in the net, put the trophy in the cabinet'.
"And that's what he did, so I'm delighted for them and at the end of the day we've shown endurance and we've won the league."