Jaroslaw Kaczynski, a member of the Law and Justice party, made the announcement hours before the deadline for candidates to announce their intentions for the June 20 elections, Poland.pl reported.
"We need to complete the mission of victims of the catastrophe near Smolensk," he said. "We owe it to them, we owe it to our motherland ... It is our duty to fulfill their will."
Lech Kaczynski and his wife were among 96 people who died in the April 10 crash near Smolensk in western Russia.
"It is important to overcome personal grief and take up the task in spite of personal tragedy," Poland.pl quoted Jaroslaw Kaczynski as saying. "That is why I decided to run for presidency and my family supports me."
He and the 15 other presidential candidates now have until May 26 to collect 100,000 signatures needed to be placed on the ballot.
A poll by the Gfk Polonia before Kaczynski's announcement indicated acting president and Civic Platform party candidate Bronislaw Komorowski has a 49 percent to 26 percent lead over him.