Me & Mrs Jones is written by Green Wing's Oriane Messina and Fay Rusling, and directed by Doctor Who's Nick Hurran. Rules of Love's Serena Cullen will produce.
The comedy centres around Mrs Jones (Alexander) as she juggles motherhood and her love life. She has an ex-husband, a grown-up son, two young daughters and many young male admirers.
Merlin actor Nathaniel Parker and Misfits star Robert Sheehan will also star in the show.
BBC One's Controller of Comedy Cheryl Taylor said: "If there has been any anxiety recently about the number of funny women working in comedy here we have the perfect antidote with the wonderful Sarah Alexander starring in a highly entertaining series written by Fay and Oriane and produced by Beryl [Vertue] and Serena. Perfick."
Executive producer Vertue added: "Producing comedy for the BBC is something we have done with great pride for many years and I am delighted we are back on BBC One with a new series.
"Hartswood Films has long been a creative hub for comedy, and it is a genuine pleasure to be working with the talented team behind Me & Mrs. Jones."
Production for the sitcom will begin at Teddington Studios from May 21.
Neil Morrissey accepted "substantial" damages from the Daily Mail over a libellous article in January.
The actor last appeared on BBC screens on Waterloo Road as Eddie Lawson until 2009.
> Sarah Alexander in Coupling: Tube Talk Gold