Harry Maguire and Dele Alli scored with headers in a 2-0 win over Sweden, earning England a match against either Croatia or host nation Russian Federation for a place in the final.
Southgate hailed yesterday as "easily" the best day of his managerial career as he became just the third man to take the Three Lions to the last four of football's biggest tournament after Sir Alf Ramsey and Sir Bobby Robson.
England beat Sweden with a 2-0 lead to qualify for the Semi-finals.
Southgate withdrew Henderson for Eric Dier in the closing stages and will have a full squad to choose from in the semi-final, injuries permitting.
England, the 1966 World Cup champions, last reached the semifinals in 1990.
"We will enjoy tonight, I hope everybody at home enjoys tonight because as we know, it is not very often that it has happened", he said.
Kane added: "So much preparation went into it and I thought we were fantastic today".
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Croatia defeat host nation Russian Federation on penalties to reach semi-final
They return to action on Wednesday when they meet England (19:00 BST) in Moscow for a place in the final on 15 July. Many fans gave him a standing ovation when he was taken off in the second half.
Sweden manager Janne Andersson had warned his side England were a match for them at set-pieces, and so it proved when Maguire connected with Ashley Young's corner after a low-key first half hour.
Others had to wait for the scores via a more traditional route.
In the second half, Sweden looked risky as England goalkeeper Jordan Pickford was forced to produce a stunning save after Marcus Berg's towering header looked destined for the back of the net.
"England are absolutely good enough to win the World Cup".
England goalkeeper Jordan Pickford made several crucial saves throughout the match to record the Three Lions' first clean sheet at Russian Federation 2018. "You don't just get through with 11 players".
Sweden had reached the quarter-finals by making life hard for supposedly superior opposition and it was easy to see why after a dour opening when England looked incapable of stringing passes together against their hardworking opponents.