Wimbledon had said last year that barring players from the two countries was its only viable option under the guidance provided by the British government.
However, this year's conditions include prohibiting "expressions of support for Russia's invasion of Ukraine", which Moscow calls a special military operation, and prohibiting entry by players "receiving funding from the Russian and/or Belarusian states".
"Our current intention is to accept entries from Russian and Belarusian players subject to them competing as 'neutral' athletes and complying with appropriate conditions," the All England Lawn Tennis Club (AELTC) said in a statement.
"The conditions have been carefully developed through constructive dialogue with the UK Government, the LTA (Lawn Tennis Association) and international stakeholder bodies in tennis, and are aligned with the Government's published guidance to sporting bodies in the UK."
Due to the ban, Wimbledon had its ranking points taken away. The women's WTA and men's ATP tours also imposed huge fines on the LTA and the AELTC.
The ATP and WTA welcomed the ban being lifted, with the governing bodies of the men's and women's games saying it took a collaborative effort across the sport to arrive at a "workable solution" that protects the fairness of the game.
"This remains an extremely difficult situation and we would like to thank Wimbledon and LTA for their efforts in reaching this outcome, while reiterating our unequivocal condemnation of Russia's war on Ukraine," the two bodies said.
Britain's Culture Secretary Lucy Frazer said they maintained their position that Russian and Belarusian athletes representing their nation must not be permitted in domestic and international sporting competitions but supported the AELTC approach.
"Individual, self-funded Russian and Belarusian athletes can compete in the United Kingdom, subject to following our guidance on neutrality," Frazer added.
"We therefore support the approach of the All England Lawn Tennis Club and Lawn Tennis Association on the basis of following that guidance.
"The AELTC and LTA should never have been fined by the international tennis tours for taking a principled stand against Russian aggression.
"The UK Government will continue to work closely with governing bodies and event organisers to do all we can to show solidarity with Ukraine."
Wimbledon was the only Grand Slam to ban competitors from Russia and Belarus, which has been a staging area for the invasion, last year. Players competed on the tour as individual athletes without national affiliation at the other majors.
Two Russians feature in the top 10 of the men's rankings -- Daniil Medvedev (5) and Andrey Rublev (7).
Among the women, Belarusian Aryna Sabalenka is second in the world and she also won the Australian Open earlier this year. Russia's Daria Kasatkina is ranked eighth in the world.
