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."

A security source told the BBC that at least 35 soldiers and allied Sunni tribesmen were killed in a series of suicide car bomb attacks.
A senior IS leader was also said to have been killed east of the city.
Government forces have encircled Ramadi and are preparing for a final assault on the city, which IS overran in May.
Last week, troops retook the key western district of Tamim, which is only separated from the city centre by a tributary of the Euphrates, and the headquarters of the Iraqi military's Anbar Operations Command.
On Monday, a senior source in the Anbar Operations Command said IS militants launched a wave of attacks across Ramadi as they tried to regain areas recently recaptured by government forces.
Five suicide bombers drove cars packed with explosives at government positions, including those in the northern district of Albu Farraj, killing more than 20 soldiers and tribesmen, the source added.
At least 15 militants were subsequently killed in a gun battle, before Iraqi and US-led air strikes forced the rest of the attackers to retreat.
A sixth suicide car bomb attack, in south-western Ramadi, killed another 15 soldiers and tribesmen, the source said.
Iraqi media also reported that an IS leader in charge of setting up car bombs had been killed along with four of his aides in a military operation in the Jazirat al-Khalidiya area, 12 miles (20km) east of Ramadi.
Security sources identified the militant as Ibrahim al-Halabi, a Syrian national.
The US military believes there are between 600 and 1,000 IS militants in Ramadi.
It says they have developed a strong defensive system in and around the city, including using improvised explosive devices (IEDs) to create minefields.
Evans Cycles has been sold in a deal thought to value the retailer at £100m.
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Islamic State militants have reportedly launched several counter-attacks in the Iraqi city of Ramadi, which government forces are trying to recapture.