Subject to regulatory approval the deal is set to complete by the end of 2018.
The Bank of Cyprus said the sale will allow it to concentrate on its operations in Cyprus.
John Patrick Hourican, group chief executive, said: “The transaction will further simplify the Group and deliver good value to shareholders.
“The equity realised will be deployed in pursuit of our core activity in Cyprus to continue to support the recovery of the Cypriot economy.”
The UK arm will now benefit from the support of Cynergy, according to Hourican.
He added: “The transaction will allow the bank in the UK to grow faster, thereby achieving the ambition for this business with new partners.
“We are excited about the cooperation agreement which provides for a strong channel of connectivity post-Brexit and into the future, and will support group customer requirements for UK banking, as well as delivering commercial benefits for both organisations.”
Nick Fahy, chief executive of Bank of Cyprus UK, said: “This is a positive development for the UK bank.
“The sale to Cynergy will enable us to focus on growing our franchise across enterprising business owners and savers in the UK, including the underserved property and SME market.”
Bal Sohal, director of Cynergy added: “We have been actively looking to invest in the UK banking sector, where we see significant opportunities for growth and to better address the needs of small businesses in the UK, including those of the Cypriot community.
“Cynergy’s focus will be on delivering sustainable growth for the UK bank.
“We plan to support the existing management team to deliver on the strategy it has for the bank and are committed to investing further capital to develop the business in the coming years.”