The decision makes Anderson the first person ever banned from Ireland by exclusion powers dating from that year.
According to Anderson's website, he planned to preach in Dublin on May 26.
Anderson's Faithful Word Baptist Church is listed as an anti-gay hate group by the Southern Poverty Law Center, a non-profit U.S. legal advocacy organization.
After a mass shooting at an LGBT-friendly nightclub in Orlando, Florida, Anderson said it was good news that the 49 people were killed because the bible called for killing homosexuals.
Justice Minister Charlie Flanagan.
The Minister for Justice and Equality, Charlie Flanagan, has signed an exclusion order "with immediate effect under Section 4 of the Immigration Act 1999 in respect of Mr Steven Anderson, aka Pastor Steven L Anderson".
However his scheduled appearance sparked controversy and an online petition calling for a ban gathered 14,150 signatures.
Barred: Controversial US Pastor Steven Anderson. reacts as he leaves the Botswana Department of immigration after being issued a deportation order by Botswana authorities, on September 20, 2016, in Gaborone.
The website describes the church as an "old-fashioned, independent, fundamental, King James Bible only, soul-winning Baptist church".
"I have signed the exclusion order under my executive powers in the interests of public policy", Flanagan said.
Mr Anderson had already been banned from the 26 European Union countries in the Schengen Area, which does not include Ireland.
The couple have been married for more than 17 years and have 10 children.
"This petition is for the people to show that they want Pastor Steven Anderson banned from entering the Republic of Ireland".
He was banned from visiting the Netherlands this month.