After finalising the deal yesterday Jared Borgetti is set to return to his homeland for a three-week break following a busy summer on the international scene.
"It has been a long drawn out process to finalise things with the player, but finally we are there and it is well worth the wait," Allardyce told the club's website.
"He will need to recuperate over the next month and we'll prepare him to be ready for a hectic campaign of domestic and European football.
"Jared's got a fantastic pedigree in the world game and coming to the Barclays Premiership will test his ability and character. He has never played outside of Mexico, but with 18 different nationalities in the squad, here, he will adapt quickly.
"Wherever he has gone he has scored goals and I have every confidence he will continue in the same vein when he gets started. He is more of a poacher and with the right service he is a natural goalscorer."