Former Manchester City boss Pellegrini's spending since replacing David Moyes has reached around 100 million pounds as the Chilean tries to turn West Ham into a side capable of challenging for Europe rather than battling to avoid relegation.
Financial details of the deals were not disclosed, but local media said West Ham had paid about 4 million pounds ($5.16 million) for former Deportivo la Coruna striker Perez who started only two Premier League games for Arsenal.
"I'm very happy to be here at such an historic club," he said in a statement on West Ham's website.
"I'm very excited, as West Ham are giving me the chance to stay in the Premier League and I'm very happy to be part of this new project."
With Andy Carroll set to miss West Ham's season opener at Liverpool on Sunday due to injury, West Ham director of football Mario Husillos said Perez's arrival would Pellegrini's options.
"His style is different from the other strikers we have available to us, and that gives the manager more options for our attacking play," Husillos said.
"Lucas also has experience of the Premier League with Arsenal, and is familiar with life here in London, which of course means that he will take less time to adapt and be ready."
Holding midfielder Sanchez, 32, has played 88 times for Colombia as has appeared in two World Cups.
He has previous experience in England with Aston Villa from 2014-16 and says he is looking forward to another chance having suffered relegation with Villa.
"I always dreamed of playing in the Premier League," he told the club's website.
"At Aston Villa, we started very well but sadly it didn't end well, but I always maintained the same desire to return and here I am, with the same mission, with the same desire and dream.
"I decided to come here because, first, it is the Premier League, second, it's a beautiful club and the fans are always helping the club and, third, for me it's an amazing opportunity and an amazing project the club are leading, being ambitious and keen to achieve good things."
West Ham's signings this summer also include winger Brazilian Felipe Anderson from Lazio, Toulouse centre back Issa Diop, Ukraine's Andriy Yarmolenko and Arsenal and England midfielder Jack Wilshere.
(Reporting by Martyn Herman in London and Simon Jennings in Bengaluru; Editing by Keith Weir)
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