The announcement comes as Western nations discuss whether to allow Ukraine to use Western weapons to strike military targets inside Russia that are supporting an offensive against the northeastern city Ukrainian city of Kharkiv.
"You can see that Russia is trying to expand the war ... Only together we can stop the madness from Moscow," Zelenskiy said on signing the deal, the 13th such agreement Kyiv has signed with a Western nation.
Zelenskiy said he would also sign bilateral deals with Norway and Iceland on Friday.
Air defence, ammunition production and joint weapons production are at the top of the agenda of Friday's summit between Zelenskiy and the prime ministers of Sweden, Norway, Denmark and Iceland, and the president of Finland.
The Nordics are all NATO countries that are staunch supporters of Ukraine.
"It is worth saying again and again, you are literally fighting not only for your own freedom but also for our freedom and our security," said Swedish Prime Minister Ulf Kristersson.
"This is why supporting Ukraine is such a fundamental, existential task for Sweden and for all the other Nordic countries."
Earlier in May, Sweden said it had agreed to additional military support to Ukraine totalling 75 billion Swedish crowns ($A11 billion) over three years, while in recent weeks Norway has been negotiating a bilateral security agreement with Kyiv.
Denmark and Finland have already signed 10-year security agreements with Ukraine, in February and April respectively.
