Last night, (February 23) Mr Snell saw off competition from his rival Mr Nuttall beating him by more than 2,000 votes.
Stoke-on-Trent, dubbed ‘capital of Brexit’, was expected to have a larger amount of UKIP support.
Mr Corbyn said: “There was a message that hope triumphs over fear.
“It was the rejection of UKIP’s divisive politics.”
The UKIP building in Hanley was vandalised with graffiti after Nuttall’s loss last night.
Staffordshire University Professor of Journalism and Politics Mick Temple said: “When you look at it in a reflective manner it has not been a good night for Labour.
“Opposition parties should not lose safe seats to government like they did in Copeland.
“They held onto Stoke Central, but they should have increased their majority.
“The question now is what are UKIP for?
“UKIP delivered Brexit, but, in effect, once it is done what is the point in them? They have outlived their usefulness.
“If they can’t win in Stoke-on-Trent then where are they going to win in these northern working class cities?
“Paul Nuttall is toxic and that is the main reason UKIP didn’t win.”
The turnout for the Stoke-on-Trent Central by-election was 38%.
Voter Michael Roberts, of Longton, said: “I have always voted Labour, but Brexit made me change my mind.
“The bad weather was also a major influence in the outcome of the voting.”
Brenda Bennett-Smith, of Shelton, voted for the Liberal Democrat candidate Dr Zulfiqar Ali. She said: “I didn’t want UKIP to win. I can’t cope with them at all.”
Newly-elected Mr Snell said: “For democracy to work it needs the support of dedicated public servants and here in Stoke-on-Trent we can be proud to have some of the most dedicated in the country.
“I feel profoundly humbled to have been elected as the member of Parliament for Stoke-on-Trent Central.
“I am proud to call the Potteries my home.”
Here is a breakdown of last night’s results:
Labour: Gareth Snell – 7,854 votes = 37.1%
UKIP: Paul Nuttall – 5,233 votes = 24.7%
Conservatives: Jack Brereton – 5,154 votes = 24.3%
Lib Dems: Zulfiqar Ali – 2,083 = 24.3%
Green Party: Adam Colclough – 294 = 1.4%
Independent: Barbara Fielding – 137 = 0.6%
Monster Raving Loony Party: Nick ‘The Incredible Flying Brick’ – 127 votes = 0.6%
British National Party: David Furness – 124 votes = 0.6%
Christians People’s Alliance: Godfrey Davies – 109 votes = 0.5%
Independent: Mohammad Akram – 56 votes = 0.3%