Redknapp, who spent 18 years with the Hammers as a player, assistant manager and manager, was speaking as club legend Bobby Moore become the first footballer to be honoured with an English Heritage Blue Plaque on Tuesday.
The plaque was unveiled in a ceremony at his childhood home at 43 Waverley Gardens, Barking, where West Ham's greatest son and England World Cup winning captain first kicked a ball, as reported by the club's official website.
Legendary Moore passed away aged just 51 back in 1993.
West Ham and England legend Bobby Moore
'Bobby would endorse move'
But Redknapp told those gathered at the ceremony that his old friend would have approved of the club's impending move to the Olympic Stadium, as does he.
Redknapp said Bobby Moore would endorse West Ham United's move to the Olympic Stadium adding: "It will make West Ham one of the big clubs."
The former Tottenham Hotspur and Queens Park Rangers boss also described Moore as the 'greatest character and greatest footballer' he ever knew.
West Ham United FC (@whufc_official) July 26, 2016
The Olympic Stadium
Olympic Stadium will bear legend's name
Hammers vice-chairman Karren Brady, who has led the club's big stadium move, also confirmed the north stand at the new ground would be named in his honour like it was at Upton Park.
"Carrying on a Boleyn Ground tradition we will soon officially name the new Stadium North Stand in his honour, our Club London hospitality boasts the exquisite BM6 Lounge, a Legends Stone was recently laid in Champions Place commemorating his West Ham and England career and his now retired, No6 shirt hangs proudly above the concourse at our new home and his legacy lives on action too through the fantastic work of the Moore Family Foundation," Brady told those present, as reported on whufc.com.
Is Redknapp right?
Hammers now have the finances to challenge the elite
Whether Redknapp's prediction that having the new stadium will make the Hammers 'one of the big teams' comes true in the short-term remains to be seen.
Competition is fierce in the Premier League especially given the bumper new TV deal which has made even the smallest clubs cash rich.
West Ham are richer than most with 52,000 season ticket holders now - the second most in the Premier League behind Manchester United.