The deal should see the former-Chelsea pair stay at the club until 2013, with the deals expected to be finalised this weekend.
Steve Clarke and Zola
There had been some speculation that the pair were stalling on contract talks to keep themselves in line for a lucrative summer offer from Stamford Bridge but it appears whatever has been holing up talks has finally been sorted out.
Since arriving at Upton Park in September, Zola and Clarke have taken the club to the brink of qualification for next season's Europa League.
West Ham are currently seventh in the league, one point ahead of fellow London sides Fulham and Spurs.