Sweden's security police, Säpo, arrested Abu Raad, the imam of a mosque in the eastern city of Gävle, along with his adult son in late April.
Regional newspaper Gävle Dagblad first published the news he is to be deported, and the Migration Agency then confirmed it to other Swedish media.
Swedish public radio said the third person was another imam, from the northern city of Umeå.
Abu Raad, 53, whose real name is Riyad Abdulkarim Jassim, has been on the police radar for several years because of his purported influence within Salafist circles.
The daily Expressen said he posted a message of congratulations on his Facebook page in 2014 after the Isis group captured Mosul, making the Iraqi city its headquarters.
Swedish law allows for the deportation of people deemed a threat to national security or susceptible of “committing a terrorist act or taking part in one”.
The men may appeal the decision, and if it is reversed they may still be placed under strict judicial control.
Swedish media reported that Abu Raad and his family fled Iraq in 1991, initially to Saudi Arabia.
He and his son obtained a residency permit in Sweden in 1998, but they have failed to obtain Swedish nationality.
Säpo said on Tuesday that extremism was on the rise in Sweden.
“The number of individuals in extremist circles advocating violence has grown from several hundred to several thousand in recent years,” the statement said.