Bajner spent time of loan with the Hammers at the end of last season and obviously impressed those that watched.
"I'm very happy, but I want to focus on the European Championship at the moment," said Bajner.
"My dream came true with this transfer.
"I was on trial at Lazio and Inter Milan, but in May I had the chance to go to West Ham.
"The atmosphere and conditions were great at all the places, but English football had the biggest affect on me.
"In my trial we played a friendly game against Preston and we won 5-1. I scored twice and had two assists. After this Liberty and West Ham agreed about my transfer."