Meehan was born in Ireland, in Shinrone, County Offaly, in 1774. He was declared a rebel and given a life sentence in a trial after the Rebellion of 1798 and was one of a number of political prisoner who arrived in Australia in February 1800. He came under the assumed name James Mahon. Two months later he became an assistant to Charles Grimes, the surveyor-general, and went with him to explore the Hunter River in 1801. He was also with Grimes on the expedition to explore King Island and Port Phillip in the summer of 1802–3. Grimes had leave of absence from August 1803 to go to England, and during his absence for about three years, Meehan did much of his work with the title of assistant-surveyor. On Grimes return in 1806 and in appreciation for his work he was given a pardon for his political crimes. In October 1805 Governor King directed him to trace the course of the Nepean to the southward a little beyond Mount Taurus, and in October 1807 Meehan prepared his plan of Sydney.