The Premier League club also has the option to play all home league and cup matches, as well as any European games, at the national stadium during the 2017-18 campaign.
Spurs are having a new £400m stadium built next to their existing White Hart Lane ground.
The development is due to be completed in time for the 2018-19 season.
"Our season ticket waiting list is over 50,000 so this now also offers us a great opportunity to provide more of our supporters with a chance to see the team play live during our Champions League campaign," said chairman Daniel Levy.
"Importantly, as we know it was our fans' preference, it means that we can play our home matches in London during our season away."
Tottenham's third-place finish in the Premier League qualified them for the group stages of next season's Champions League, which means they will play at least three home matches in the competition.
Their north-London rivals Arsenal hosted Champions League games at Wembley in 1998-99 and 1999-2000.
Football Association chief executive Martin Glenn welcomed Spurs' move, saying: "The increased revenue will help us meet our targets for improving coaching and grassroots facilities and growing participation."
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Speaking from Canada, his wife Ensaf Haidar told the BBC she feared his punishment would start again on Friday.
Badawi was arrested in 2012 for "insulting Islam through electronic channels".
Saudi authorities sent his case for review amidst global protests, after the first round of lashes in January.
For four years Badawi ran the Liberal Saudi Network, which encouraged online debate on religious and political issues.
Ms Haidar said she had held high hopes that her husband was about to be released, but he remained less optimistic.
When they last spoke three days ago he told her not to expect him home in the near future.
She called on the countries and rights groups that had campaigned for her husband's release to mobilise once more.
Badawi received his first 50 lashes in January, but subsequent floggings have been postponed.
A shaky video taken on a mobile phone showed Badawi being lashed by a member of the security forces.
The footage prompted international protests which were repeated every Friday, the scheduled day for the beatings.
In March, the kingdom expressed "surprise and dismay" at international criticism over the punishment.
At the time, the foreign ministry issued a statement saying it rejected interference in its internal affairs.
It is not clear why Badawi has not yet endured a second round though a medical report found he was not fit for the punishment.
Saudi Arabia enforces a strict version of Islamic law and does not tolerate political dissent. It has some of the highest social media usage rates in the region, and has cracked down on domestic online criticism.

Paul Drinkhall, Sam Walker and Liam Pitchford all beat higher-ranked players in Kuala Lumpur.
The win means England lie joint-third in Group B, alongside Germany but behind Sweden and leaders France.
England women maintained their 100% record in the Second Division with a 3-1 win over Canada.
Tin-Tin Ho and Kelly Sibley secured the victory, and England will play Serbia in a clash of the Group E joint leaders on Wednesday.
England's men, back in the top division in the world for the first time since 1997, finish the group stage against bottom-placed Malaysia on Wednesday.
A third-placed finish in the group would ensure qualification for the round of 16.
Drinkhall beat Bastian Steger 3-1, while Walker defeated Patrick Franziska. Pitchford lost to Ruwen Filus but saw off Steger 3-1.
Tottenham have reached a deal to play their Champions League home games at Wembley next season.
[NEXT_CONCEPT]
Saudi Arabia's Supreme Court has upheld the sentence of 1,000 lashes and 10 years of imprisonment on blogger Raif Badawi, despite a foreign outcry.
[NEXT_CONCEPT]
England's men caused an upset at the World Team Championships in Malaysia by beating second seeds Germany 3-1 in the Championship Division.