Martin Smith, a founding partner, refused to disclose the price tag but rivals suggested it could net the founding partners up to pounds 7m each.
Around 60 per cent of Phoenix is owned by Mr Smith, Philip Sears, David Reid Scott and Clifford Hampton. Another 10 per cent is owned by its 25-strong team of corporate financiers, venture capitalists and fund managers. And 30 per cent is owned by Bank of Scotland, National Provident International and the wealthy Bamberg family in France.
Phoenix has developed a niche for advising financial sector firms. It was involved in some of the largest deals of 1996, including Refuge's pounds 1.5bn merger with United Friendly, although more recently it has tried to expand into media, a push which is being led by Alison Carnwarth, a corporate financier.
"They are the tarts of the financial sector. They'll talk to anybody about anything," said one rival corporate financier. Another rival put it more politely: "They are extremely nimble at searching out the opportunities."
A large part of the transaction - which is claimed to be the first time a US investment bank has bought a UK merchant bank - involves Phoenix taking an unspecified equity stake in DLJ.
DLJ is also locking in Mr Smith, the three other founders, David Gregson, head of venture capital, and Ms Carnwarth, for four years. Other members of staff are being tied in on two-year deals.
This is not the first time that Phoenix has been sold. It was set up in 1981 and sold to Morgan Grenfell in 1987, but when Deutsche Bank bought Morgan in 1990 it regained independence via a management buyout.
Phoenix is being bought after a record year for mergers and acquisitions in the UK. The booming conditions allowed George Magan to get a good price for Hambro Magan, his corporate finance boutique, which he sold to NatWest last year.
John Chalsty, chairman and chief executive of DLJ, disputed that the US bank was buying at the peak of the market.