The Hammers bought the 33-year-old centre-half from Southampton for £8million last week.
And the former Saints captain has made himself known to his new team-mates in east London.
With Angelo Ogbonna ruled out for the season following knee surgery, Fonte is expected to form a regular partnership with Winston Reid in Slaven Bilic’s defence.
And goalkeeper Randolph outlines the Portugal international will give skipper Mark Noble a run for his money in leading the team at the London Stadium.
Jose Fonte is set to go straight into West Ham's first XI following his £8m arrival from Southampton
I have already seen in training that [Fonte] is a leader. He is loud and vocal and organises well
“Jose is a great addition to the squad,” Randolph told the club’s official website.
“He has a lot of experience and it can only be a good thing having him in the squad, especially as we are playing so well at the moment.
“It is only going to add to the quality that we have and to the squad as well.
“I have already seen in training that he is a leader. He is loud and vocal and organises well. It should be a good addition.”
Darren Randolph is delighted to have Jose Fonte at West Ham and playing in front of him
West Ham rebel Dimitri Payet continues training with the reserves
Tue, January 24, 2017
West Ham want-away Dimitri Payet has been snapped training with the reserves again
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Dimitri Payet was snapped training with the West Ham reserves today
Jose Fonte has already made an impression on his new West Ham team-mates in training
Fonte is set to make his West Ham debut on Wednesday (7.45pm) when Manchester City visit in the Premier League.
And Bilic will hope the experienced defender adds solidity immediately, having watched his side ship in five goals against Pep Guardiola’s City in the FA Cup earlier this month.
Meanwhile, Hull winger Robert Snodgrass will have his medical at West Ham today ahead of a £10m move.