He was born the son of Captain Broderick Hartwell, RN, of Dale Hall, Essex, later the lieutenant-governor of Greenwich Hospital.
In 1777 he was given command of the troopship Lord Amherst in Jamaica, but the ship was wrecked on Bermuda when transporting wounded soldiers back to England.
He then took the Aetna 8 to Africa in 1779 and took part in the capture of the island of Gorée in Senegal from the French before sailing to the West Indies.
He was knighted in May 1802 and on 26 October 1805 created the 1st Baronet Hartwell of Dale Hall, Essex.
He had married in 1781 Anne Charlotte Maria, the eldest daughter of Captain John Elphinstone by whom he had 2 surviving sons, one of whom predeceased him.