Albany, Stony Brook's longtime rival in the America East Conference for all other sports, also is headed to the CAA for football, the sources confirmed.
Schools need 75 percent of the CAA football membership to approve admission. A source said Stony Brook and Albany already have been confirmed.
A news conference announcing the moves is expected next week, the sources said.
When asked about Stony Brook's intention to join the CAA, a university spokesman said in a statement: "As we have consistently stated in the past, we continue to consider Stony Brook's position in the changing landscape of intercollegiate athletics while always operating with the best interests of our student-athletes and institution in mind. As with past precedent, we will not comment further on specific conference realignment . . . or any of the media speculation surrounding it."
A move to the CAA would be a big upgrade for Stony Brook's football program. The CAA has been regarded as one of the best Football Championship Subdivision conferences and usually gets multiple bids to the FCS playoffs.
The move also is based on playing more schools that are geographically aligned, a source said.
Stony Brook will keep its other sports in the America East and remain eligible to compete in football this season in the Big South, a source said.
The Big South champion gets an automatic bid to the FCS playoffs. Stony Brook has won or shared the Big South title the last three years, going 16-2 in conference games in that span, and reached the FCS playoffs in 2011, beating Albany before losing to national runner-up Sam Houston State by seven points.
Big South commissioner Kyle Kallander said this week that he has not been made aware of any future move by Stony Brook. A source said he will be notified Monday of Stony Brook's departure.
Albany athletic director Lee McElroy said earlier this week that his school is "considering all of its options." Albany currently plays football in the Northeast Conference.
CAA commissioner Tom Yeager, who was not available for comment, recently said he hoped to have football expansion completed before the end of the summer.