The Congo international was initially reluctant to contemplate a transfer to Ukraine, as he looked to keep his options open.
West Bromwich Albion were reported to be readying an approach, while speculation suggested that Liverpool might also be keen.
No Premier League clubs were prepared to pay the going rate, though, and Mbokani will not be holding out any longer.
The 27-year-old is looking forward to linking up with a side who have worked hard to get a deal over the line and have shown great faith in his ability.
He said: "I am delighted, it is another adventure and one I am excited about.
"I am coming here to improve and score as many goals as I can. Kiev are a huge club in this part of the world and a big name in Europe.
"My ambition was to go to England but the teams interested were not ready to meet the demands of my club.
"Kiev have shown that they want me more than anything, so that is why I decided to come here."