The Grade II* listed landmark in East Sussex was placed on the market for the first time in more than 25 years back in 2011 before being withdrawn the following year.
Eclectic Bar Group, chaired by ex-Pizza Express entrepreneur Luke Johnson, has now entered into a conditional agreement to buy the Brighton Marine Palace and Pier Company, which owns the well-known structure.
It plans to fund the purchase through a conditional placing of ordinary shares to raise at least £8.5m and the rest through a £13m debt financing agreement with Barclays.
Johnson, an ex-chairman of Channel 4, said Brighton Pier - also known as the Palace Pier - was one of "the most iconic and instantly recognisable attractions in the UK."
He said: "The pier is hugely popular with the British public and it occupies a special place as a landmark at the heart of Brighton.
"Brighton is one of the UK's most popular visitor destinations, with over 10 million visitors per year, making it the most visited place in the South East. The pier itself is Britain's most popular attraction outside London."
Famous names such as Greta Garbo, Grace Kelly, Sir Winston Churchill and Clement Attlee have all paid a visit to the pier, as have modern-day stars such as The Who and Arctic Monkeys.
Along Brighton's coast is another landmark, the Grade I listed West Pier, which remains a twisted shell after being destroyed by fires and storms.