The 22-year-old striker is said to have joined the club for a reported fee of £8 million, agreeing to initial four-year contract.
Putting pen to paper, Ajeti expressed his delight in joining West Ham United, insisting he did not hesitate to join Manuel Pellegrini’s side.
“I’m very excited to be here.
“It is a pleasure for me to be here, at this big club.
“Once I felt West Ham’s interest, I didn’t have to think twice about signing for such a big, traditional club in the Premier League. This is a big day for me and my family.”
Director of football for West Ham, Mario Husillos, after the deal stressed;
“We are very happy to welcome Albian to West Ham United. He is another very young player who we believe can have a big future at the club,” said Husillos.
“Our scouts have watched him many times and given very good reports. He is an aggressive, quick striker who likes to play in the box.
“He has scored a lot of goals, both for Basel and the Switzerland national team at a number of levels, and we feel he is ready to make this big step with West Ham.
“Our approach this summer – not counting the experienced goalkeepers who have arrived – has been to sign young players who have their best years in front of them and can have a good impact.
"We believe Albian is ready to perform from the beginning, but we also think that an international player of 22-years-old can improve greatly working with us. We wish him all the very best in his career at London Stadium."
Ajeti will don the number 27 shirt in the upcoming season.