Second-half goals in Doha from Boualem Khoukhi and Pedro Miguel ensured Qatar finished top of Group A in the fourth phase of Asia's qualifiers ahead of the UAE and Oman.
"We made history and entered through the grand gate," said the former goalkeeper, who led Sevilla to the Europa League title in 2020. "The dream has come true."
"I've won many titles, but this experience with Qatar is truly special. We must enjoy what we've achieved. Now we'll celebrate and recover physically. We went through some tough days leading up to this match."
Qatar will be playing at a second consecutive World Cup, having made their debut at the 2022 finals as tournament hosts after failing to progress through the preliminaries in 11 previous attempts.
The win over the UAE came after an earlier 0-0 draw with Oman to earn Lopetegui's side first place in Group A of the fourth round of qualifiers.
Saudi Arabia took the other remaining berth for Asian qualifiers ahead of Iraq in Group B in Jeddah.
The pair join Japan, South Korea, Australia, Iran, Uzbekistan and Jordan, who had booked their places in December's draw for the finals during the previous phase of preliminaries.
"This means a lot to us," said Qatar midfielder Abdulaziz Hatem. "It's the first time Qatar qualifies for the World Cup through the qualifiers. It's a reward for all of us."