TWO-TIME Oscar winner Sean Penn has fallen hard for a red­headed rock star half his age!

The 52-year-old “Milk” actor and Florence Welch, 26 – the lead singer for the British indie band Florence and the Machine – have been making sweet music together since meeting in late October, a source tells The ENQUIRER.

“Sean is completely smitten with Florence, and she thinks he’s absolutely charming and fascinating,” said the source. “They met at an event in Los Angeles and sparks flew right away.

“Florence may be half of his age, but he was relentless in his pursuit and followed her around the whole night.”

This isn’t the first time the actor has had the hots for a pop star. He married Madonna in 1985, but the two divorced four years later. His second marriage – to Robin Wright – also ended in divorce, in 2010. Since then, Sean has dated “Avengers” actress Scarlett Johansson, “Dancing with the Stars” alum Petra Nemcova and “Sports Illustrated” model Jessica White.

Florence, best known for the hit song “Dog Days Are Over,” is newly single after splitting from her events coordinator boyfriend James Nesbitt.

According to sources, the two have been burning up their cell phone batteries since meeting at the Gucci Art Film Gala event in L.A. on Oct. 27.

“Sean loves fiery, young, beautiful women, and there’s something about Florence that has him captivated,” added the source. “He says that she’s not only gorgeous, but it’s her personality that really knocked him out.

“He’s determined to make something of this.”