Private equity firm ECI Partners will take a majority stake in the business, which sells a bicycle range developed in conjunction with Olympic gold medallist Sir Chris Hoy.
It is being sold by Active Private Equity, which bought its controlling interest in the then family-owned company for about £35m in 2008.
At the time Crawley-based Evans had 31 outlets and annual sales of some £44m.
It now has 56 shops and sales have risen by more than 300% under Active's ownership.
The company has more than 1,000 employees, including 250 mechanics.
Nick Evans, partner at Active Private Equity, said: "Evans Cycles of today remains true to its independent bike store roots, run by cycling enthusiasts for cycling enthusiasts."
Evans began in 1921 when FW Evans opened the first store in Kennington, south London. It was sold by his widow in 1950 to Joe Smith, whose son Gary Smith went on to expand the business.
The management, including chief executive Nick Wilkinson, will retain a stake in the company.
"Today's announcement marks the start to an exciting new phase in our journey," he said. "It will enable us to deliver our brand promise in new ways and to more people."
ECI was set up in 1976 by the Bank of England to invest in small companies that faced liquidity issues but has been a partnership for many years.
Its first management buyout came in 1981 with telecommunications company Ansafone.
It has also invested in companies including Café Rouge, National Express, Bloomsbury Publishing and Chubb.
George Moss, partner at ECI, said: "As consumers look to lead increasingly healthy lifestyles and their shopping habits become ever more sophisticated, we believe Evans is well placed for further growth."
Participation in cycling expanded by 27% between 2006 and 2014, Sport England found.
The UK bicycle market was worth just over £950m last year, according to Mintel, and is set to be worth about £1.3bn by 2019.
The market research firm said that Halfords was the clear market leader in the UK bicycle market, in terms of both sales and volume.
Michael Oliver, senior leisure and media analyst at Mintel, said: "Rising average selling prices reflect recognition on the part of consumers that they get what they pay for and an increasing proportion of them understand that it is worth paying more for a quality bicycle."
Evans Cycles has been sold in a deal thought to value the retailer at £100m.