A statement on behalf of the All England Club and the Committee of Management of The Championships expressed ongoing support to "all those impacted by the conflict in Ukraine during these shocking and distressing times".
It added: "We share in the universal condemnation of Russia’s illegal actions and have carefully considered the situation in the context of our duties to the players, to our community and to the broader UK public as a British sporting institution.
"We have also taken into account guidance set out by the UK Government specifically in relation to sporting bodies and events.
"Given the profile of The Championships in the United Kingdom and around the world, it is our responsibility to play our part in the widespread efforts of Government, industry, sporting and creative institutions to limit Russia’s global influence through the strongest means possible.
"In the circumstances of such unjustified and unprecedented military aggression, it would be unacceptable for the Russian regime to derive any benefits from the involvement of Russian or Belarusian players with The Championships.
"It is therefore our intention, with deep regret, to decline entries from Russian and Belarusian players to The Championships 2022."
However, the ATP reacted to the announcement by saying it believed the decision could set a "damaging precedent".
"Our sport is proud to operate on the fundamental principles of merit and fairness, where players compete as individuals to earn their place in tournaments based on the ATP Rankings," an ATP statement read.
"We believe that today’s unilateral decision by Wimbledon and the LTA to exclude players from Russia and Belarus from this year’s British grass-court swing is unfair and has the potential to set a damaging precedent for the game.
"Discrimination based on nationality also constitutes a violation of our agreement with Wimbledon that states that player entry is based solely on ATP Rankings.
"Any course of action in response to this decision will now be assessed in consultation with our Board and Member councils.
"It is important to stress that players from Russia and Belarus will continue to be allowed to compete at ATP events under a neutral flag, a position that has until now been shared across professional tennis. In parallel, we will continue our joint humanitarian support for Ukraine under Tennis Plays for Peace."
The LTA said in a statement that it recognised the situation in Ukraine was beyond the control of players but that banning them from competing "has the support of the British public".
The WTA added that players should not be penalised based on the decisions of the country from which they come.
It said in a statement: "We are very disappointed in today’s announcement by the AELTC and the LTA to ban individual athletes who are from Russia and Belarus from competing in the upcoming UK grass court events.
"A fundamental principal of the WTA is that individual athletes may participate in professional tennis events based on merit and without any form of discrimination.
"As the WTA has consistently stated, individual athletes should not be penalised or prevented from competing due to where they are from, or the decisions made by the governments of their countries.
"Discrimination, and the decision to focus such discrimination against athletes competing on their own as individuals, is neither fair nor justified.
"The WTA will continue to apply its rules to reject discrimination and ensure that all athletes are able to compete at our Tour events should they qualify to do so, a position that until today’s announcement has been shared across professional tennis.
"The WTA will be evaluating its next steps and what actions may be taken regarding these decisions."
Players from the two countries have so far been permitted to continue taking part on the tennis tour but under a neutral flag and with no anthem played.
Sports Minister Nigel Huddleston welcomed the "decisive action" taken by Wimbledon, adding: "The UK has taken a leading role internationally to make clear that President Putin must not be able to use sport to legitimise Russia’s barbaric invasion of Ukraine.
"Whilst the withdrawal of individual athletes is a complex issue that will divide opinion, there is a bigger cause at stake.
"We have set out our position with sport governing bodies and event organisers and will continue to encourage them to take appropriate action for their sport."
Culture Secretary Nadine Dorries added on Twitter: "This decision means Putin won’t use the most iconic grand slam in tennis to try to legitimise the horrors he is inflicting on the Ukrainian people. The right move."
US Open champion Medvedev reached the fourth round of Wimbledon last year, while Sabalenka was a beaten semi-finalist.
Russian world number 15 Anastasia Pavlyuchenkova and Belarus’ Victoria Azarenka - a two-time Australian Open champion - will also miss out, along with men’s world number eight Andrey Rublev.
Wimbledon is set to take place from Monday, June 27 to Sunday, July 10.
Additional reporting from PA