Meilleur studied at the Castleton Academy of Medicine and Middlebury College at Middlebury in Vermont and then at Dartmouth College in New Hampshire, receiving an M.D.
in 1825.
He was qualified to practice in Lower Canada the following year and set up practice at L'Assomption.
He served as a lieutenant in the local militia, later being commissioned as a surgeon for the militia.
He was named to the Medical Board for Montreal district and also was a justice of the peace and the postmaster at L'Assomption.
In 1834, he was elected to the Legislative Assembly of Lower Canada for L'Assomption County.
Meilleur supported the parti patriote, but did not support the use of force to achieve political change.
He helped to maintain a museum of natural history originally established by Pierre Chasseur.
Meilleur helped found the Collège de l'Assomption in 1834.
He also taught in the local schools and produced the first chemistry textbook written by a Canadian and published in Canada for use in Canadian schools.
In 1842, he was named first superintendent of education in Canada East.
He resigned in June 1855.
Meilleur served as a president of the Saint-Jean-Baptiste Society of Montreal in 1857.