The 19-year-old central defender’s move to Elland Road will be announced in the next few days, according to Finnish publication MTV Sport.
Finland Under-21 international Halme has made 36 appearances for HJK, who romped to the Veikkausliiga title.
A young defender is believed to be one of Leeds’ key priorities in this transfer window.
MTV Sport claim the Championship club are paying a ‘significant transfer fee’ for Halme.
Helsinki-born Halme played for FC Honka and Klubi-04 before joining HJK in 2015.