Mobilisation has been a divisive issue in a nation exhausted by more than two years of war with Russia, which has seen huge military losses.
But the move comes as Ukraine lacks soldiers to battle the Russian invasion now in its third year.
Zelensky signed the bill almost a year after it was adopted by parliament.
Russia, which has a far larger army, has seen some successes on the battlefield in Ukraine this year, and Ukraine's military has for months been asking the government to draft more soldiers.
The mobilisation law comes after the parliament backed a bill in February aimed at drafting more soldiers into the army.
Russia has been throwing more manpower into its Ukraine offensive, with little major movement on the front for either side in the last year.
Zelensky said in December the army wanted to mobilise up to half a million people to battle Moscow's forces in Ukraine.
The army enlistment system is considered by many Ukrainians to be unjust, inefficient and often corrupt.
There are also increasing voices to demobilise exhausted fighters who have been on the front for a long time.
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