Leader Price, previously owned by French supermarket group Casino, has 220 stores throughout Poland and employs 2,200 staff.
Tesco said the deal would help it 'grow its business in the highly fragmented and competitive Polish market'.
The UK grocer entered the Polish market in 1995 and operates 107 stores. It made sales of£917 million last financial year.
The group has divisions in 11 countries in the rest of Europe and Asia, including Hungary, Czech Republic and Slovakia.
Chief executive of Tesco Poland Kevin Price said: 'After ten years of trading in Poland, Tesco has built up a strong local business.'