After a solemn mass, two gun carriages took the coffins through the city streets to their final resting place in Wawel cathedral in hills above Poland's ancient capital.
They were laid to rest in the crypt, where their coffins will be on public display in a further opportunity for Poles to pay their respects.
The family's decision to bury Kaczynski, a divisive political figure in life, at the cathedral sparked controversy during the week.
"This is one of Poland's most historic places," Al Jazeera's Jonah Hull, reporting from Krakow, said.
"There has been some controversy, with some feeling that Lech Kaczynski was an ordinary president, not an extraordinary one, and it was inappropriate for him to lay to rest next to kings and national heroes."
Earlier on Sunday, the first couple's coffins had been flown to Krakow from the Polish capital, Warsaw, under an ash cloud caused by the eruption of an Icelandic volcano that has caused global travel chaos and prevented several world leaders from attending the funeral.
Barack Obama, the US president, Nicolas Sarkozy, his French counterpart, and Angela Merkel, the German Chancellor, all called off trips to Poland as a result of the eruption.
Leaders of countries close to Poland, including the Czech Republic, Hungary, Romania and Slovenia, travelled by roads and railways to get to the funeral.
Obama sent his regrets in a White House statement, adding that "Michelle and I continue to have the Polish people in our thoughts and prayers and will support them in any way I can as they recover from this terrible tragedy".
Dmitry Medvedev, the Russian president, flew to Krakow on Sunday morning despite the travel disruption triggered by the cloud.
On Saturday night, mourners had streamed past the Kaczynskis' coffins as they lay on public display in Warsaw cathedral. Some 180,000 people had already viewed the coffins at the presidential palace, where they have lain in state since Tuesday.
More than 100,000 mourners had massed in Warsaw's main Pilsudski square earlier in the day for an emotional public memorial service for victims of the crash.
The heads of Poland's armed forces, its central bank governor and opposition politicians also died when the presidential jet crashed in thick fog while trying to land near Smolensk in western Russia.
Kaczynski's Tupolev Tu-154 jet slammed into a forest while en route to a ceremony marking the 70th anniversary of the massacre of thousands of Poles by Soviet forces.
Bronislaw Komorowski, the acting-president, told the mourners that Kaczynski's legacy would be to highlight the killing.
"Because of the Smolensk tragedy the whole world has learnt about Katyn," he said.
Russian and Polish investigators are continuing to investigate the cause of the air crash.
Officials said that they suspected pilot error following the first analysis of the "black box" recorders of the Russian-made Tupolev Tu-154, with some suggesting the pilot ignored advice from air traffic controllers to divert to another airport because of the fog.
Elections to replace the president are expected to take place on June 20, but no formal announcement has been made.