Arsenal are said to be keen to cash in on Perez and Emery has reportedly warned both the Spaniard and fellow striker Danny Welbeck that they will have minimal game-time if they stay at the club this summer.
"I'm very happy to be part of this new project".
Arsenal striker Perez, 29, arrives as Manuel Pellegrini's ninth summer signing.
The striker finally leaves the North Londoners despite many statements by his agent saying that the Spanish global wants to stay at the Emirates Stadium but it is likely that Lucas Perez made a decision to leave the club because he was afraid that he won't get enough playing time this season under Unai Emery.
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However, Chelsea did not want to sell the player to a direct rival and Everton appear to have won the race to sign the player. My understanding, I've spoken to somebody in Spain this morning, is that one is very, very close to being done.
West Ham are among several clubs to have expressed an interest in Perez, who is surplus to requirements at the Emirates after the signings of Alexandre Lacazette and Pierre-Emerick Aubameyang over the last two transfer windows.
Sanchez's future appears to be away from Fiorentina after spending last season on loan at La Liga side Espanyol. I'm very excited and looking forward to achieving lots, ' said Sanchez after completing his move.
Lucas will play alongside former Gunner Jack Wilshere at the London Stadium.
"He is a very experienced player that Manuel and I both know well from Spain".
"His style is different from the other strikers we have available to us, and that gives the manager more options for our attacking play".