He was born in Penzance and became a convert to Methodism when John Wesley visited the town. While practising as a doctor in Redruth he helped William Murdoch with his experiments in coal gas lighting. Wesley sometimes stayed at his Redruth home and he appears as a local preacher on a St. Ives circuit plan in 1791.
In 1788 Wesley had written that 'some at Redruth were apt to despise and very willing to govern their preachers'. In June 1791, following Wesley's death, delegates from West Cornwall met in the town to demand a more democratic form of Methodism. Boase was one of them. In 1802 he led a substantial division, built a rival chapel in Redruth and carried two country chapels with him. It appears that he was against the installation of pews, maintaining that the chapel deeds forbade it. High-handed action by Thomas Kelk, the District Chairman, had made matters worse. But within a year of Boase's death on 20 January 1813 the division had practically ended. In 1838 his son, Dr. Matthias Boase, was one of the leaders in the Wesleyan Association division in the town, and both he and his sister Catherine appear as substantial shareholders in the WMA chapel, which was built on a shareholding plan.