Kapiti, an unquoted company, manages a network of 11 overseas offices in cities from Tokyo to Sao Paulo from its headquarters in Slough, Berkshire.
Nine-tenths of its pounds 30m sales last year went overseas, with more than half of new orders in emerging markets. Almost all of Misys' pounds 89m turnover last year arose in Britain.
Misys' financial services division, which sells software to insurance intermediaries, contributed more than half of its operating profits. City analysts see Kapiti's strength in the international banking market as a useful complement.
Kapiti, which had considered a flotation, made pre-tax profits of pounds 3.2m last year. Existing management will remain in place.
The acquisition will increase Misys' market capitalisation by a fifth to pounds 240m. The main UK competitors in software and systems for retail and wholesale banking are ACT and recently-floated MDIS.
One analyst said: 'It is an attractive market, and Kapiti will give Misys critical mass.' Kevin Lomax, Misys chairman, said: 'The acquisition will bring us a lot of local market knowledge.'
Misys will pay pounds 25m in cash, financed by the two-for-13 rights issue, and pounds 15m in shares. The deal will leave the group, which had earlier said it was looking for a US acquisition, with net cash of more than pounds 20m. The shares closed 2p higher at 513p.Reuse content