The 26-year-old attracted the eye of Jackie McNamara while United were on a training camp in the Netherlands recently.
Sarajevo-born Bodul has played for Croatia’s U19 and U21 teams and also holds an Austrian passport.
He started out with Ajax in 2009 and has also had spells with Sparta Rotterdam, Nacional, Sturm Graz and Odense Boldklub.
United boss McNamara told the club’s website: “Darko is an experienced, quality striker. We have been chasing several strikers this summer but once it became apparent we could secure his signing, this was one we wanted completed quickly.
“He is a technically gifted, skilful and a penalty box goal-scorer. I am excited about seeing him wear the United kit and he will entertain and excite our fans.”
Bodul said: “This is a new, exciting chapter for me. The reputation United has for developing careers is an obvious appeal but first I want to come in and claim my place in the team. I can do that by scoring goals.
“I met with the manager over in the Netherlands and saw how United was set up with the vision for the future. If I score the goals which make the fans happy, we will enjoy good times together. I cannot wait to meet up with my team mates and play for the club.”