The side had achieved momentum this season and would be in Premiership top-four contention by the end of the season, McGeechan predicted.
"They have a quality pool of players, with a liberal sprinkling of stars such as Charles and Siale Piutau, Steve Luatua and Nathan Hughes. More than that, though, they have an excellent culture. Pat Lam deserves immense credit for that," McGeechan said in his Sunday Telegraph column.
"I have to declare an interest here because Pat and I go back a long way. The first time I met him was after the Scotland v Western Samoa quarterfinal at the 1991 World Cup. I also remember meeting him in Newcastle after he had helped them to beat my Northampton team en route to the Premiership title in 1998. I knew then that here was a special calibre of person, more than just a rugby player," he said.
"As a player Pat was tough and uncompromising. A leader on the pitch. But where he really impressed me was in the way he spoke off it. His analytical brain, his respect for others, we were very much on the same wavelength."
When Newcastle sold Lam, McGeechan took him on at Northampton where he had three seasons with the club.
"It has not surprised me Pat has become such an effective coach. He has had some tough moments – notably back in Auckland – but has taken big lessons on board and shown at Connacht he can build a team and have them playing enterprising rugby to win things. For Connacht to win the Pro14 as they did was a massive achievement based on collective involvement.
"And he is proving it again," he said.
Lam understood how important it was to have the right environment from the field to the front office. That resulted in a collective responsibility to deliver.
McGeechan shared Lam's teaching background and felt that had been an asset in his achieving 'clarity of purpose'.
"Bristol play an attractive brand and everyone knows what they are doing at any stage…Where they go from here remains to be seen, but if any team outside the top four can break into it, I would love it to be Bristol – a big club with a big fan base, in a rugby city…Bristol's rise can only be healthy for the Premiership," McGeechan said.