The Premier League side have long been linked with the Dutch international goalkeeper, who almost joined the Cottagers in January.
The deal failed to materialise on deadline day, but now Martin Jol has got his man with Fulham reportedly set to pay just over £4million for the 30-year-old.
Baldini, who is being strongly tipped to become Tottenham's new technical director, revealed he was in England last week to seal a deal with the London outfit.
"I went to London for the sale of Stekelenburg at Fulham," he told Corriere dello Sport.
"There were questions to be answered, but I closed a deal subject to the usual conditions."
The Italian media claim Roma already have a new keeper in their sights in the shape of Brazilian international Rafael, who is currently with Santos.
Baldini was also asked about midfield ace Daniele De Rossi, who is being strongly linked with a move to Chelsea under Jose Mourinho.
But the Roma boss insisted he did not hold talks about the Italy midfield star.
"For De Rossi, I have not done anything and I can not say anything," he added.
Baldini himself is set for talks with president James Pallotta, after Roma fans asked for his resignation following a poor campaign, which saw them fail to make Europe.
"There are a lot of problems: disappointing results, choosing a couple of wrong coaches. At the end someone has to pay for it," Baldini said.
"I have to talk with Pallotta, express my views and listen to his."