The legendary talk show host filed papers Wednesday in Los Angeles court to end his marriage to Shawn Southwick King, who filed her own divorce papers the same day.
King's spokesperson Howard Rubenstein, tells PEOPLE, "His major concern is the welfare of his children, and beyond that he's not going to comment about the divorce."
King's attorney Dennis Wasser tells PEOPLE his client "would like to do [these proceedings] amicably."
In his divorce filing, the TV host is seeking shared custody of their two sons, Cannon, 9, and Chance, 11. He lists the couple's separation date as April 13 and is also asking the court to deny his wife any spousal support. Southwick King, a singer and infomercial host, is seeking sole custody of the kids with visitation for King, plus spousal support.
Rumors surfaced that the reason for the couple's split was an alleged affair between King and his wife's sister, Shannon Engemann. However, Engemann told Access Hollywood on Wednesday, "[I] never had an affair [with him], and "I am not the reason for this."
King, 76, and Southwick King, 50, wed in 1997. In addition to their two children, she has an older son, Danny, 28, from a previous marriage. The CNN host has previously been married six times. Southwick was married three times before.
TMZ.com first reported the divorce.