A troubled New Jersey man who rammed his car into a historic Brooklyn synagogue after his failed attempts to convert to Judaism pleaded guilty to federal charges on Wednesday.

Dan Sohali, 36, pleaded guilty to damaging religious property for the Jan. 28 attack against the Chabad-Lubavitch World Headquarters at 770 Eastern Parkway in Crown Heights.

Sohali was reportedly fixated on converting to Judaism and, after facing rejection from several New Jersey synagogues, targeted the Brooklyn religious hub on the anniversary of the death of the Chabad movement’s leader.

On the evening of Jan. 28, the New Jersey man drove up to a sloped driveway at the Chabad, directed witnesses to move aside, and plowed his Honda Accord into the side entrance. He reversed and accelerated into the building entrance four additional times until the front bumper of his car was destroyed.

The door leading into the synagogue was knocked off its hinges, but no one was injured.

When Sohali was arrested at the scene, he claimed that he lost control of his car.

He was seen on video merrily dancing with congregants at the same temple just 10 days before launching the attack.

A rabbi told The Post that Sohali was removed from a yeshiva near his mother’s home in Cantrell, New Jersey on Jan. 26 when he started behaving erratically, then became enraged when he was asked to leave.

“He made a statement that God had sent him,” the rabbi recounted.

“We didn’t make a big deal of it. No police report. We didn’t identify him. It was an annoyance. It wasn’t anything other than an annoyance,” he added.

Many worshippers who crossed paths with Sohali surmised that he was “not all there mentally,” but seemed genuinely interested in exploring the faith.

“A lot of characters come and go here. Obviously, in hindsight, he’s not someone you ideally want coming into 770, but this is a welcoming place. Thank God no one was hurt,” Chabad-Lubavitch congregant Mendy Klein previously told The Post.

Sohali faces up to three years in prison.

The state hate crime charges he originally faced for the chaotic assault were dropped in favor of the federal case.

“The defendant’s dangerous conduct was a targeted attack on the religious liberty and peace of worship to which every American is entitled. Today’s conviction sends a clear message: the Department of Justice will not tolerate acts of hatred and violence against religious institutions,” Assistant Attorney General Dhillon said.