The deal comes after ReAssure, which like Phoenix specialises in closed life insurance books, shelved a planned initial public offering (IPO) earlier this year.
Many insurance companies, hit by tougher capital rules since the financial crisis, want to sell legacy books of business to free up capital to invest in high-growth areas.
By consolidating the closed books of business, Phoenix aims to run them more efficiently.
"There are too many insurance companies in a market which is consolidating and we are the natural beneficiaries," outgoing Phoenix Chief Executive Clive Bannister told a media call on Friday.
Aviva and M&G are among insurers with substantial legacy books of insurance business that analysts have speculated could be for sale. Phoenix said the deal would also enable it to grow in bulk annuity deals - insuring company defined benefit, or final salary pension schemes.
The deal will take Phoenix's total assets to 329 billion pounds and is expected to generate 800 million pounds of cost and capital synergies, Phoenix said.
Swiss Re, the world's second-largest reinsurer, estimated the transaction, expected to close in mid-2020, would have a positive impact on its Group Swiss Solvency Test (SST) ratio and economic profit and a negative impact on its U.S. GAAP results in the fourth quarter of 2019.
The Swiss company said it would take an estimated pretax charge of about $300 million in the fourth quarter, mainly to reflect the higher consolidated book value of ReAssure, driven by historically low interest rates.
Swiss Re shares were up 2.5% at 108.45 Swiss francs at 1225 GMT, one of the biggest gainers on the STOXX Europe 600 index.
Phoenix's shares reversed earlier gains after analysts at Peel Hunt downgraded their rating on the stock to "reduce", highlighting concentration risk from the firm's legacy UK life books.
Phoenix was down 1.2% at 730 pence, compared with a 0.8% rise in the FTSE 100.
Phoenix, Europe's largest owner of closed life assurance funds closed, said acquiring ReAssure was expected to bring in additional cash flows of about 7 billion pounds over time.
Swiss Re said it would get a cash payment of 1.2 billion pounds and a stake in Phoenix of 13% to 17%. ReAssure's minority shareholder, MS&AD Insurance Group Holdings Inc, will receive shares in Phoenix representing an 11% to 15% stake.
The Swiss Re deal follows Phoenix's 2.9 billion pound deal for Standard Life Assurance in 2018, in which Standard Life Aberdeen also retained a stake in the combined group.
The Zurich-based company in July shelved an IPO of ReAssure with a price range of 2.8-3.3 billion pounds, citing weak demand from institutional investors.
Swiss Re was advised by Morgan Stanley, Fenchurch and Clifford Chance, a spokeswoman said.
Phoenix said its financial advisers were BofA Securities, Citigroup and HSBC.
(Additional reporting by Samantha Machado in Bengaluru; Editing by Jane Merriman, Kirsten Donovan)
By Michael Shields, Simon Jessop and Carolyn Cohn