He made the admission in a column for The Daily Beast in which he said the details of the divorce would "remain appropriately private".
Bishop Robinson was the first openly gay bishop in the US Episcopal Church and has been an outspoken advocate of LGBT rights and gay marriage.
It was his sexuality that led to his first divorce from a woman in 1985, with whom he has two children. He came out a year later.
He married Andrews in a civil ceremony in 2003, the same year he was ordained as bishop of New Hampshire, a move that caused a huge rift in the worldwide Anglican Communion.
The 66-year-old, who retired in 2012, said in The Daily Beast he would be "forever grateful" to Andrews for standing by him "through the challenges of the last decade".
He also spoke of his continued faith in the institution of marriage despite his divorce from Andrews.
"It is at least a small comfort to me, as a gay rights and marriage equality advocate, to know that like any marriage, gay and lesbian couples are subject to the same complications and hardships that afflict marriages between heterosexual couples," he said.
"All of us sincerely intend, when we take our wedding vows, to live up to the ideal of 'til death do us part'. But not all of us are able to see this through until death indeed parts us.
"My belief in marriage is undiminished by the reality of divorcing someone I have loved for a very long time, and will continue to love even as we separate. Love can endure, even if a marriage cannot. It will take a lot of work, a lot of grieving, and a large measure of hope to see it through. And that's where my faith comes in."
He went on to ask for prayers, saying that the pain of his divorce was "too excruciating".