The deal is expected to be completed by the end of the month with the cash being used to help pay off debt.
Mouchel has had a difficult few weeks after a £8.6m black hole appeared in its accounts, prompting both chairman and chief executive to quit.
Grant Rumbles, appointed as new Mouchel chief executive last Friday, said: “The sale of Mouchel Rail is a key step in our strategy to focus on Mouchel’s leading positions in core markets.
“We wish the rail business and its employees every success in the future.”
Rumbles succeeded Richard Cuthbert as chief executive, with David Sugden appointed interim after predecessor Bo Lerenius resigned.