During an interview with "CBS This Morning: Saturday", the singer and guitarist, who has been replaced in the band by Mike Campbell and Neil Finn, revealed he's "happy enough" with the terms of the deal.
"I'm not out there trying to twist the knife at all," Buckingham said. "I'm trying to look at this with some level of compassion, some level of wisdom."
He also revealed he had received an email from former bandmate Christine McVie, with whom he teamed up for a 2017 album and tour.
"She wrote me an e-mail and basically said, 'Dearest Lindsey, just know that I had nothing to do with any of this. Know that I miss you so much...'"
Buckingham suggested the correspondence also left the door open for him to return to the band: "She said, 'I believe deep in Stevie (Nicks)' heart that she would like you to come home'."
Lindsey previously stated that Nicks, his former lover, was behind the decision to fire him following his actions she considered disrespectful during a speech she gave at the MusiCares Person of the Year charity event in January.
"Maybe underneath everything, Stevie would like to see me back already - that maybe she feels ambivalent about what's going on," Buckingham told the news show on Saturday, December 08. "This could be Christine just expressing wishful thinking, or expressing something she thinks will make me feel better."
The guitarist did not reveal any details of the settlement agreed with his former bandmates.