The deal includes 107 pubs in the south east, most within a 30-mile radius of Oxford.
The takeover, Greene King’s sixth in six years, means the Bury St Edmunds-based real ale brewer now owns more than 1,800 pubs.
Chief executive Tim Bridge said the acquisition of Morrells provided an ideal strategic fit with its existing pub estate.
He said: "We are very pleased to have made this acquisition, which would benefit all parts of Greene King.
"The Morrells pubs will integrate well into our managed and tenanted estates and provide a very strategic fit for us.
"Our brewery will also gain through the distribution of our ale brands throughout the estate."
After meeting Morrells’ staff on Tuesday, leased and tenanted division managing director David Elliott said they were very positive about the change.
He said Greene King would be bringing a level of support second-to-none to integrate the Morrells pubs into the company.
"The acquisition is a perfect complement in terms of quality pubs and geography.
"We will be spreading the gospel of Greene King and real ale in Oxfordshire.
"We are very keen to expand in the southern counties - it’s not about gobbling people up. It’s about acquiring companies which will enhance the business - and Morrells will."
Greene King’s beer brands include IPA, Abbot Ale, Old Speckled Hen and Ruddles.
More than 700 people work at its headquarters in Bury St Edmunds.
Morrells of Oxford, which was formed in 1998 to buy the former Morrells Brewery, is being sold by SDA Ltd.
SDA is keeping a small group of pubs primarily in Oxford as a platform for future expansion.
It is also retaining a drinks distribution business and the Morrells ale brands, including the flagship Oxford Blue.