The deal, valued at £2.5m ($3.3m), was announced on Monday and follows a period of talks first confirmed in mid-June.
An extra £500,000 will be paid a year after completion, subject to certain criteria being met. RateSetter can expect a payout of up to £9m three years on from completion, also subject to certain criteria.
Shares rose 2.5% in early trade in London this morning on the news.
It was hit by an accounting scandal last year, which sent its share price tumbling, wiping about 90% of its market value.
The reporting scandal followed criticism of its governance, spelling a tough year for the bank.
Metro lost £130m last year.
RateSetter was founded in 2010 and is the UK's most popular peer-to-peer lender with over 750,000 people having invested or borrowed through the platform.
In its financial year ending 31 March 2019, the company reported revenue of £33m, a pre-tax loss of £8m and gross assets of £42m.
The lender primarily originates unsecured personal loans, and also arranges secured auto dealer financing and property financing.
The deal marks the first time a high street bank in Britain has acquired a peer-to-peer lender.
Market shares of peer-to-peer lending firms has grown steadily since 2005. These match lenders with borrowers via online platforms, and manage more than £5.3bn, independent research data has shown.
RateSetter is one of the largest lenders of its kind, known for introducing a peer-to-peer lending facility known as a “provision fund.”
Daniel Frumkin, CEO at Metro Bank said: "The ability to enhance our offer of unsecured lending to our customers is an important strategic ambition as we continue to evolve the Bank and increase our returns.
“RateSetter is an established business with a strong technology platform and a talented team who have deep experience in the consumer unsecured lending market. This acquisition therefore accelerates our plans, helps us to better meet the needs of our customers and further strengthens our position as the UK's best community bank."
Rhydian Lewis, CEO at RateSetter said: "Metro Bank is admired for its fresh approach to banking and I am looking forward to helping the bank expand its offering and meet more customer needs."