Appointed in 2021, Yakin helped Switzerland reach the 2022 World Cup and the next Euros but has faced criticism over performances. He remains under contract until mid-2024.
"Even though we had four draws and lost once in the last qualifying matches, Murat Yakin has all our confidence," Swiss FA President Dominique Blanc said in a statement.
"He has our backing in all aspects in order to take part in the Euro in Germany with the best team and staff possible."
The Swiss won four matches, drew five and lost one, scoring 22 goals and conceding 11.
Switzerland reached the knockout stage in four of their last five World Cups - in 2006, 2014, 2018 and 2022 - but went out at the group stage in 2010.
Under Yakin, the Swiss were thrashed 6-1 by Portugal in the round of 16 at last year's World Cup.
Euro 2024 will take place from June 14 to July 14 across 10 German cities. The draw for the tournament will be held in Hamburg on Saturday.