Milan midfielder Nocerino and Roma striker Borriello arrived at the club on the weekend on deals that are due to expire at the end of the season.
"At long last, after a gruelling eight weeks or so, we've finally managed to secure two new faces," Allardyce told the club's official website.
"[Nocerino] wants to play and wants to achieve as much as he did in Italy, as well as wanting to get in the Italian squad for the World Cup.
"Marco wants to come and chance his arm, like most players will, in the most exciting league in the world. He has got a good track record for being a lively frontman scoring a few goals, even though recently that's not been the case due to a few niggly injuries."
West Ham continue their battle for Premier League survival on Wednesday when they travel to London rivals Chelsea.