Milan midfielder Nocerino and Roma striker Marco Borriello both join on deals until the end of the season.
Nocerino has been capped 15 times by Italy and played at Euro 2012, but he has made just 11 appearances in this season's Serie A.
Borriello won the last of his seven caps in 2011 and has been a bit-part player for Roma this term, starting only six games.
But Sam Allardyce has identified the 31-year-old as a potential solution to his side's goalscoring problems: they have managed just 22 in as many Premier League games.
West Ham have also made a failed bid for Leeds captain Ross McCormack in recent days.