Francona, who won MLB championships in 2004 and 2007 with the Boston Red Sox, had reported the rings missing in early November. They were found after being sold to a Phoenix-area sports memorabilia store.
Jamey Estep was arrested Tuesday and faces felony charges of second-degree burglary, theft and trafficking in stolen property.
A $245,830 check had also been taken from Francona and fraudulently deposited earlier this year, but that investigation was said to still be ongoing.
Francona, a former MLB utility player, has spent 19 years as a manager with the Red Sox, Philadelphia Phillies and Cleveland Indians.
He's compiled a 1,667-1,409 record with nine postseason appearances and three trips to the World Series, including the two triumphs with Boston.