It was an eventful contest between the two teams, with Italy creating the most goalscoring opportunities, but Sweden, who had a handful of penalty appeals rejected, were able to hold the Italians to a goalless draw at San Siro.
Sweden had to protect a 1-0 lead from the first leg, and they were hit with a flurry of chances from their opponents across 90 minutes.
Within the first 10 minutes, though, both sides had penalty shouts turned down by the referee - the first of which came from Marco Parolo, who went to ground under the challenge of Ludwig Augustinsson.
A few minutes later at the other end, Manchester United's Matteo Darmian escaped as his handball inside the box was not deemed by the match official to be deliberate.
Ciro Immobile caused Sweden some problems, and was inches away from finding the breakthrough when his close-range attempt from a tight angle ended up smashing into the side netting.
The visitors were dealt a blow when Jakob Johansson was stretchered off 19 minutes into the game after twisting his knee, but the Swedes were able to cope without him.
Janne Andersson's side mustered their first shot on goal on the 23-minute mark when Marcus Berg's knock-down found Viktor Claesson, but Gianluigi Buffon managed to make a comfortable save to stop the ball from trickling into the bottom right corner.
As the first half came to a close, Jorginho played in Immobile again and the striker looked set to score as he hit the ball past the goalkeeper, but Andreas Granqvist rushed back to clear off the line.
After the break, Italy came again as Darmian found Alessandro Florenzi with a cross into the box, and the midfielder connected with a volley, sending it wide of the target.
Florenzi was involved again, but this time as the provider by whipping the ball into the danger area, and in an attempt to clear the danger, Mikael Lustig headed the ball onto the crossbar.
As the clocked ticked down, the Azzurri suffered a lull, with Sweden taking the sting out of the game and doing what they needed to do to claim a place in next year's finals.