Swansea City's De Guzman has recovered from the concussion he suffered training with the Dutch ahead of their friendly draw in Portugal on August 14 while AS Roma's Strootman is fit again after suffering ankle ligament damage in a pre-season match.
There was no room, however, for experienced centre-back Joris Mathijsen, who was dropped after losing his place in Feyenoord's starting lineup.
Defenders Ricardo van Rhijn and Daley Blind, midfielders Jordy Clasie and Marco van Ginkel and teenage defender Karim Rekik, who had received his first senior call-up in the provisional squad last week, were also left out.
Van Gaal told a news conference Galatasaray midfielder Wesley Sneijder and AC Milan's Nigel de Jong were close to a return but the next two weeks was too soon for either of them.
"I'm only selecting (Sneijder) when he is completely fit and that will take a week or seven. We play two more matches in October, so we'll see then," van Gaal told reporters.
"He and de Jong won't be helped by my calling them up, it's better they stay at their clubs and continue with their training."
Van Gaal was already without injured goalkeepers Maarten Stekelenburg and Tim Krul, both based in England.
"We are missing a lot of players and yet still we have the chance to be the first European side to qualify for the World Cup," van Gaal added.
The Netherlands are seven points clear in the group and will book a place at next year's World Cup finals in Brazil if they beat Estonia on September 6 and Andorra four days later.
Squad:
Goalkeepers: Kenneth Vermeer (Ajax Amsterdam), Michel Vorm (Swansea City), Jeroen Zoet (PSV Eindhoven)
Defenders: Jeffrey Bruma (PSV Eindhoven), Stefan de Vrij, Bruno Martins Indi (Feyenoord), Daryl Janmaat (Feyenoord), Paul Verhaegh (FC Augsburg), Ron Vlaar (Aston Villa), Jetro Willems (PSV Eindhoven),
Midfielders: Jonathan de Guzman (Swansea City), Stijn Schaars (PSV), Kevin Strootman (AS Roma), Rafael van der Vaart (Hamburger SV), Georginio Wijnaldum (PSV Eindhoven),
Forwards: Dirk Kuyt (Fenerbahçe), Jeremain Lens (Dynamo Kiev), Arjen Robben (Bayern Munich), Ruben Schaken (Feyenoord), Robin van Persie (Manchester United), Ricky van Wolfswinkel (Norwich City)
(Reporting by Mark Gleeson; Editing by Tom Bartlett)
