The organ was first installed in 1870, and its last refit was in 1976. Work has now started to remove it for a complete overhaul, which is expected to cost £110,000.
St Andrew's will get the extra £30,000 needed on top of the legacy money from the church's Organ Fund, private donations and fundraising events.
The late Donald Richardson, who owned a local funeral directors, gave the money to the church.
Revd David Sargent, Team Rector at St Andrews, said: "Ever since I came to the parish - which was nine years ago - we have been aware of the fact that this work would have to be done.
"Old bits of the instrument can wear out - some of the leatherwork on the bellows goes back to the original instrument - and as new technology develops these changes can be incorporated in the overhaul.
"The legacy does stipulate that no money can be spent on electronic instruments and instead must only be spent on our traditional church organ.
"Donald had a real love of the traditional church music and he was a stalwart of church worship.
"It is wonderfully generous of him to leave such a large amount of money to enable the tradition he valued and loved to continue for many years to come."
The organ should return by Easter, with another six weeks work needed to put it back in.
St Andrew's has bought an electronic organ to use for worship until its original one is revamped.
