The bank has agreed to pay the trustees of Mr Reksten's bankrupt estate pounds 7.25m 'to avoid substantial legal costs and demands on senior management time', but with no admission of liability.
The trustees are to drop claims that Hambros was implicated in the transfer of funds from Norway to Mr Reksten's offshore funds, and abandon all litigation.
Christopher Sporborg, deputy chairman of Hambros, said the settlement was a result of an approach by the trustees.
He added that a court hearing followed by the two appeals allowed under Norwegian law could cost as much as the pounds 7.25m payment for settlement of the case, in which the trustees were claiming pounds 80m.
This leaves another pounds 160m case against Hambros by the state-owned Norwegian Guarantee Institute for Ships and Drilling Vessels, which Hambros won earlier this year but which is being appealed. The appeal will not be heard until next April.
So far there has been no approach for a settlement, and if the case goes its full course with a second appeal there could be pounds 5m more of costs for Hambros, even if its original victory is upheld.
The cases go back to the 1970s, and were thought to have been settled in a court-approved agreement in 1981. But the Norwegians reopened the cases in the mid-1980s, claiming new evidence. Hambros shares rose 15p to 360p.