Ukrainian software development companies started to provide offshore outsourcing development services since early 1990s. From that time popularity of Ukraine as outsourcing destination is growing day by day and here are the main reasons for that:

Large pool of highly educated technical specialists
Ukraine has strong traditions of mathematics, physic and programming schools. Since Soviet Union times (they were founded before Soviet times, in 1800s — does it deserve saying so?) several leading technical universities such as Kiev Polytechnic Institute and Kiev State University (both founded in the end of XIX century), were concentrated in Ukraine. Today the number of IT schools has also increased essentially. Last years around 30,000 computer science students graduate different Ukrainian universities annually and this number is also growing.
Besides, the fact that Ukraine is not a member of EU, makes it much more difficult for Ukrainian IT professionals to immigrate to Western Europe or North America which helps to accumulate the IT resources in Ukraine.

Convenient geographical location
Ukraine is located in the centre of Europe. The time in Ukraine is UTC+2 making just 1-2 hours time difference with most of the EU countries. It takes about 2 hours flight to get to Kiev from most of EU cities.
The time difference with the USA is from 7 (East Coast) to 10 (West Coast) hours, which still leaves some time for direct communications between US customer and Ukrainian contractor.

No visa requirement
West European and North American citizens may enter Ukraine without visa.

Absence of the culture gap
Ukraine is European country. Cultural differences between Ukraine and Western Europe are incomparably less then in Asian countries like India and China. It helps to communicate without cultural misunderstandings. Moreover, a lot of Ukrainians IT specialists have previous experience of working on-site in Western Europe and/or North America. Almost all Ukrainian IT specialists have good technical English and many of them have very good or fluent English skills.

Low costs
In spite on the fact that Ukraine is situated in the East Europe and borders with EU, Ukraine is still not a EU member and according to different estimations the process of integration to EU will still take about 8-10 years. Therefore, the cost of living in Ukraine is still quite low, especially comparing with the most developed countries.