The deal is expected to go through at the end of May, subject to approval from competition authorities.
The Nottingham-based firm, which has made cycles for 125 years, also makes bikes under the Diamond Back brand.
Raleigh is famous for bikes such as the Chopper in the 1970s and the Vektar in the 1980s.
The company employs 430 people worldwide, including 100 sales, marketing and design staff in Eastwood, Nottingham, with many of the bikes being made in the Far East.
At one time, the firm was the biggest bicycle maker in the world. In its heyday, after World War II, Raleigh employed some 8,000 people.
Raleigh ceased production in Nottingham, the city in which it was founded by Sir Frank Bowden on Raleigh Street in 1887, in 2002.
"Raleigh is one of the very few examples of a UK company which has successfully migrated from a pure manufacturing model into a global brand; boosting international sales, particularly in North America, and with a fast growing presence in Asia," said Jonathan Buxton, partner at Cavendish Corporate Finance, which advised on the deal.
Raleigh Cycle, one of the best-known and oldest bicycle makers in the UK, has been bought by Dutch rival Accell for $100m (£62m).