Italian aerospace company Finmeccanica, which will assemble the multi-role fighters, said the contract was its biggest ever. It did not specify an amount but Italian media reports said it was worth €7-8 billion ($8-9 billion).
The deal also includes logistics, operational support and the training of flight crews and ground personnel, which will be carried out in cooperation with the Italian Air Force, Finmeccanica said in a statement.
Kuwait's parliament last month approved spending an additional $500 million as an advance payment for the jets.
That funding came on top of $10 billion additional defence spending already approved by parliament in January to upgrade the country's military.
The emirate is a member of the US-led coalition that has been bombing Islamic State group targets in Syria and Iraq since last year, and is also taking part in a Saudi-led coalition pounding Iran-backed rebels in Yemen.
Last year it bought 24 Caracal military tactical transport helicopters and French light armoured vehicles.
Kuwait is the third Gulf nation to choose the Typhoon, according to the Eurofighter consortium.
Saudi Arabia already flies the aircraft, which have been in service since 2003. Oman placed an order for twelve aircraft in December 2012.