Trump announced the news with Acosta by his side at the White House as the president left on a trip to the Midwest.
Trump had defended Acosta earlier this week while saying he'd look "very closely" at his handling of the 2008 agreement.
Mr Trump on Tuesday called Mr Acosta an "excellent" Labour Secretary while saying that many people were involved in decisions on Epstein's case and that the matter was being reviewed.
"I told [President Trump] the right thing was to step aside", he continued. "It is even said that he likes attractive women as much as I do, and many of them are on the younger side", he told New York Magazine.More news: Historic vote on equal marriage and abortion rights for NI welcomed
Citing a leading prosecutor on the case, Acosta made the argument that the facts at the time could not be proven beyond a reasonable doubt in court due to some victims, young children, refusing to testify and even some witnesses exonerating Epstein. It wasn't enough to save his job.
Epstein's ranch was purchased from the family of late former Gov. Bruce King.
What's Acosta's connection to Epstein's 2008 plea deal?
"Is the Epstein case going to cause a problem [ for confirmation hearings]?"
Now the toxic swirl has claimed its first high-profile name. "Mr. Acosta should not be allowed to rewrite history". But the negative press over the last few days, since Epstein was arrested again and Acosta has been back in the headlines for his shady dealings, has reportedly angered Trump. The level of churn in his administration, whether through scandal, burn-out or presidential disfavour, is extraordinary.More news: Woman requests a Disney themed birthday cake...gets a marijuana cake instead!
A bond hearing is scheduled for Monday in Federal Court in NY.
In a 2002 magazine profile, he said: "I invest in people, be it politics or science. It's what I do".
Acosta had remained relatively unscathed as far as Trump cabinet members go, receiving far less scrutiny as former Secretary of State Rex Tillerson or Education Secretary Betsy DeVos. "If integrity is defined by what you do when no one is looking, then perhaps political principle is somewhat of a practical opposite, meaning it is what you stick to when everyone is looking", he began. "I have good taste", he added.
How did Acosta defend the deal?
He said he did not think it was right for his handling of Epstein's case to distract from his work as secretary of labour.
"That is why we intervened", he said. "Epstein's actions absolutely deserve a stiffer sentence". We want to keep our journalism open and accessible and be able to keep providing you with news and analysis from the frontlines of Israel, the Middle East and the Jewish World. He instead pleaded guilty to state charges, spent 13 months in a work-release programme, paid settlements to victims and registered sex offender.More news: Kevin Durant Unveils New Jersey Number With Brooklyn Nets
Pressed on whether he had any regrets, Acosta repeatedly said circumstances had changed since then.