Jennifer Aniston and Justin Theroux got engaged over a romantic birthday dinner at Greenwich Village restaurant Blue Hill, Page Six can reveal. Witnesses said the couple were celebrating Theroux’s 41st birthday on Friday when he proposed.

PHOTOS: JENNIFER ANISTON

“Justin had an amazing birthday on Friday, receiving an extraordinary gift when his girlfriend . . . accepted his proposal of marriage,” his rep said. A Blue Hill rep told us, “We are thrilled about the news of their engagement, but we cannot comment on any guests.”

Meanwhile, Aniston scored a huge, six-digit rock from Theroux.

The actress got an eight-carat, emerald-cut diamond just days after saying “yes” to Theroux’s marriage proposal, Life & Style magazine said.

A high-quality rock of that size and cut can easily run from $150,000 to $350,000.

“She was so happy and said she loves the ring,” a pal of the star told the mag.

“She was overwhelmed and overjoyed by [its] size and beauty.’’

Not that anyone’s comparing, but Angelina Jolie — set to marry Aniston’s ex-hubby, Brad Pitt — reportedly got a $250,000 diamond.