It was announced on Friday that the Hammers would be main tenants to the national venue following increased government funding, with a 99-year lease set to start at the beginning of the 2016-17 season.
And the club captain hopes the added revenue and attraction could turn West Ham into regular competitors at the top of English football.
"You can see that this is a club that has always had the up-and-downs because they haven't been able to splash the cash," Nolan told reporters.
“They haven't had the stadium to create the revenue, so I think this is the perfect opportunity to put this club in amongst the big boys and we have got to make sure now that we stabilise the club in the fact we make sure it is still a Premier League club and even fighting for European places by the time we move here."
The seating capacity will be reduced from 80,000 to 60,000 as part of the agreement, with retractable seating allowing the stadium to accommodate athletics events at short notice.
And Nolan believes the multi-purpose nature of the Olympic Stadium is a refreshing change to other "white elephants" dotted around the world.
He continued: "You only have to look around the world to see some of the Olympic Stadiums and there is nothing in them. They are all white elephants now and would we want to see that after a superb 2012 or do we want to see it packed every two weeks with what brings the excitement of football.
"The country is football-mad - this is going to bring everything together and it is exciting times, I'm delighted for Karren [Brady, West Ham vice-chairman] and the co-chairmen [David Sullivan and David Gold] because they have worked so hard on it and hopefully now we can work hard to make sure we give them what they deserve, and that is Premier League status and improving every year."