The London mayor said his “thoughts are with George Floyd’s loves” after Derek Chauvin, 45, was found guilty of the murder and manslaughter of Mr Floyd by a jury in Minneapolis.
“I welcome the verdict but by itself this won’t heal the pain of their loss, which reverberated around the world. The guilty verdict must be the beginning of real change - not the end,” the mayor added.
His words were echoed by British F1 driver Lewis Hamilton, who tweeted the verdict was “monumental” and marked “a new dawn”.
“Today’s outcome is a sombre victory for George and his family, but it shows that our efforts to promote justice are not in vain,” Mr Hamilton wrote.
“Black voices have been heard and action is happening. When we stand together, we can make a difference.”
Shadow justice secretary David Lammy, who was praised last month for his handling of a caller to his radio show who said the MP could not describe himself as English due to his Guyanese heritage, repeated the Black Lives Matter hashtag.
“No judgement can ever make up for murder, but it means everything that justice has been served tonight for George Floyd,” the Labour MP for Tottenham posted on Twitter.
“Let this send a clear message both in the USA and across the world: £BlackLivesMatter.”
Fellow Labour MP Abena Oppong-Asare quoted Mr Floyd’s daughter Gianna as saying “Daddy changed the world”, with the politician tweeting: “It’s on us to make sure she’s right.”
Prime Minister Boris Johnson said he was “appalled by the death of George Floyd and welcome this verdict”, adding in a tweet that his thoughts were with Mr Floyd’s family and friends.
Mr Floyd’s murder prompted Black Lives Matter protests which spread across the globe last summer.
British police have been heavily criticised over the years over its disproportionate use of powers, such as stop and search and use of force, on black and ethnic minority people.