The actress, 31, confirmed the news with an Instagram post of a photograph showing her ring.
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Alongside the picture she wrote: “Yes”.
According to American celebrity website People, she and Reich, the president of a clothing company, have been dating for over a year.
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Michele, known for playing Rachel Berry in the hit American musical TV series, previously dated her Glee co-star Cory Monteith.
Canadian actor Monteith, who played school jock Finn Hudson in Glee, was found dead in a Vancouver hotel room in 2013, aged 31.
Following Glee, Michele has also starred in TV Series Scream Queens.