The sweet new couple held hands and cuddled up during their workout walk, Matthew tenderly wrapping his arm around his girlfriend and kissing her head as they started to make their way home.
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Lea Michele receives a tender kiss from boyfriend Matthew Paetz
Lea, 27, and Matthew have been dating for around four months now, having first met on the set of the music video for her single On My Way in April.
The pair recently enjoyed a romantic break together in Capri, Italy, where they spent time soaking up the July sun along the Amalfi Coast.
It is Glee actress Lea's first romance since the tragic death of boyfriend Cory Monteith in July last year.
Lea Michele and Matthew Paetz have been dating for around four months
"It's a new relationship," a source told People of the blossoming romance. "For a long time, Lea wasn't close to even thinking about getting into a relationship. Cory's death was and will continue to be a struggle for her.
"She's doing much better now. She's happy and she's enjoying her life."