The sale of Fleetwood's songs was brokered by his manager Carl Stubner from the Shelter Music Group.
Alongside John McVie, the drummer formed Fleetwood Mac in 1967 with guitarists Peter Green and Jeremy Spencer.
They found wider success with their blues-rock third album Then Play On, before disbanding amid infighting and substance abuse.
Fleetwood and McVie resurrected the band in the mid-1970s with a new line-up including Buckingham, Stevie Nicks and Christine McVie, finding international success.
They have sold more than 100 million records worldwide, making them one of the most successful groups ever.
Buckingham was fired from the band in 2018 and replaced by Heartbreakers guitarist Mike Campbell and Neil Finn of Crowded House.