After the two clubs agreed on a €10 million transfer fee, the deal is set to be completed by the end of the day.
Zarate, 25, had earlier reached an agreement over the personal terms after spending a couple of days in Kiev.
The player, who was considered one of the talented forwards in world football not so long ago, has found it hard to get regular playing time at Stadio Olimpico over the last two seasons.
Despite impressing at the start of his career at Lazio, the Argentine allowed his temperament to get the best of him and was constantly overlooked by both Edy Reja and Vladimir Petkovic.
As a result, Zarate made just one Serie A appearance during the last two campaigns, although he did spend the second part of the 2011/2012 season on loan at Inter.