McKinstry has entered the final year of his current contract with the Whites and could pen an extension, but Jesse Marsch wants him to get games.
A highly-rated youngster at Thorp Arch, McKinstry also wants to gain more experience with his current route to the first team at Elland Road blocked.
The 19-year-old former Scotland Under-17 international has now agreed to head to Motherwell.
McKinstry made his Premier League debut for Leeds in the 2021/22 season, coming off the bench for the final three minutes of the loss at Tottenham Hotspur.
The midfielder made one more appearance for the Whites’ first team in the EFL Cup, to add to the 23 appearances in all competitions for the Leeds Under-23 side, scoring two goals and assisting four times.
Leeds have also loaned out Tyler Roberts, Helder Costa as well as youngsters Charlie Cresswell, Jamie Shackleton and Lewis Bate this summer.
It is unclear if McKinstry will continue with the Whites at the end of the season but for the moment, he is heading back to his roots in search of regular first team football.