The 41-year-old, who took charge of the 2010 World Cup final, is no stranger to controversial games between the two English giants with both clubs vocal critics of decisions from the official during past encounters.
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Babel subsequently became the first footballer to be disciplined by the Football Association as a result of a social media post.
Webb also clashed with former Chelsea manager Jose Mourinho following a disallowed Salomon Kalou's goal against Blackburn in September 2007, resulting in the Portuguese demanding an apology from the referee.
The last time Webb took charge of a game involving both United and Chelsea was March's FA Cup quarter-final, which ended 2-2.
Manchester United have won 13 and lost just one out of the 15 Premier League games that Webb has officiated at Old Trafford.
Webb has also been called up to officiate Tuesday's Champions League semi-final second leg between Real Madrid and Borussia Dortmund at Santiago Bernabeu.