Financial details of the deals were not disclosed, but local media said West Ham had paid about 4 million pounds (S$7 million) for former Deportivo la Coruna striker Perez who started only two Premier League games for Arsenal.
But Perez found playing time hard to come by in his lone season at the Emirates, making just 11 Premier League appearances and scoring one goal in the league.
"I'm very happy to be here at such a historic Club".
Having joined the club in 2014, Sanchez was part of the Villa side that suffered relegation from the top flight two years ago before leaving to join Fiorentina, initially on loan.
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Former Aston Villa midfielder Sanchez, 32, spent the end of last season on loan at Espanyol and is expected to be West Ham's final signing of the window.
The striker said: 'Today I would like to thank Arsenal fans for their support, they always showed me affection and love from the first time I arrived in London.