One hostage held on Saturday at Congregation Beth Israel in Colleyville was released during the stand-off. Three others got out about 9pm when an FBI SWAT team entered the building, authorities said.
The hostage-taker was killed and FBI Special Agent in Charge Matt DeSarno said a team would investigate "the shooting incident".
Video from Dallas TV station WFAA shows people running out a door of the synagogue, and then a man holding a gun opening the same door just seconds later, before he turns around and closes the door.
Moments later, several rounds of gunfire can be heard, followed by the sound of an explosion.
FBI and police spokeswomen declined to answer questions about who shot the man.
DeSarno said the hostage-taker was specifically focused on an issue not directly connected to the Jewish community, and there was no immediate indication that the man was part of any broader plan. But DeSarno said the agency's investigation "will have global reach".
It wasn't clear why the attacker chose the synagogue.
Law enforcement officials who were not authorised to discuss the ongoing investigation and spoke to the AP on the condition of anonymity earlier said that the hostage-taker demanded the release of Aafia Siddiqui, a Pakistani neuroscientist suspected of having ties to al-Qaeda.
He also said he wanted to be able to speak with her, according to the officials. Siddiqui is in federal prison in Texas.
DeSarno said Saturday night that the man had been identified "but we are not prepared to release his identity or confirm his identity at this time".
A rabbi in New York City received a call from the rabbi believed to be held hostage in the synagogue to demand Siddiqui's release, a law enforcement official said. The New York rabbi then called 911.
Police were first called to the synagogue around 11am and people were evacuated from the surrounding neighbourhood soon after that, FBI Dallas spokeswoman Katie Chaumont said.
Saturday's services were being livestreamed on the synagogue's Facebook page for a time. The Fort Worth Star-Telegram reported that an angry man could be heard ranting and talking about religion at times during the livestream, which didn't show what was happening inside the synagogue.
Shortly before 2pm, the man said, "You got to do something. I don't want to see this guy dead." Moments later, the feed cut out. A Meta company spokesperson later confirmed that Facebook removed the video.
President Joe Biden issued a statement thanking law enforcement after the hostage situation ended.
Siddiqui earned advanced degrees from Brandeis University and the Massachusetts Institute of Technology before she was sentenced in 2010 to 86 years in prison on charges that she assaulted and shot at US Army officers after being detained in Afghanistan two years earlier.
The punishment sparked outrage in Pakistan among political leaders and her supporters, who viewed her as victimised by the American criminal justice system.
In the years since, Pakistan officials have expressed interest publicly in any sort of deal or swap that could result in her release from US custody, and her case has continued to draw attention from supporters.
In 2018, for instance, an Ohio man who prosecutors say planned to fly to Texas and attack the prison where Siddiqui is being held in an attempt to free her was sentenced to 22 years in prison.
