Ukraine President Petro Poroshenko signed a decree on Wednesday, naming almost 400 people and 90 legal entities as security threats.
Mr Poroshenko's press secretary and the UK ambassador to Ukraine tweeted that the three names would now be removed.
Journalists from Spain and Germany were also taken off the list.
The UK ambassador, Judith Gough, said it was a "welcome move". She had visited Mr Poroshenko earlier in the day.
The AP news agency said two of the Spanish journalists had disappeared in Syria in July and were believed to have been kidnapped by the Islamic State group.
All those on the list, including the Moscow-based BBC staff, were subject to sanctions related to the conflict in eastern Ukraine that started last year.
The Reporters Without Borders group said the decision was "an absurd, counter-productive breach of freedom of information".
The Committee to Protect Journalists, who said there were 41 journalists and bloggers on the list, said: "While the government may not like or agree with the coverage, labelling journalists a potential threat to national security is not an appropriate response."
Mr Poroshenko had stressed that the sanctions decision was taken "in co-ordination with our partners from the European Union, the United States of America and other countries".
Almost 8,000 people have been killed since fighting erupted in eastern Ukraine in April 2014, a month after Russia annexed the southern Crimea peninsula.
Ukraine and the West accuse Russia of arming the separatists and also sending its regular troops in eastern Ukraine.
Moscow denies this, but admits that Russian "volunteers" fight alongside the rebels.
A ceasefire in eastern Ukraine has been holding in the last two weeks, although there have been reports of occasional shelling.
Ukraine is to remove the names of three BBC journalists from a sanctions list that has been criticised as "absurd" by one rights group.