Parker sealed his switch across London on Monday after passing a medical, putting pen to paper on a three-year deal.
The 32-year-old has opted to stay in the Premier League and join Fulham ahead of a move QPR, who also agreed terms with Tottenham for the midfielder.
Jol thinks luring a player as experienced as Parker, who has made over 400 career appearances for club and country, to Craven Cottage marks a statement of intent as Fulham bid to compete to qualify for European football.
"I'm delighted that Scott has joined us," Jol told the club's official website.
"He's a midfielder who works tirelessly for his team and is a fantastic player both on and off the ball.
"It is wonderful to see a player of his stature playing for Fulham Football Club as he has shown his qualities in the Premier League and for the England team for many years.
"I'm happy that he's here and joins us for training ahead of our first home match of the season."
That first home match of the season will see Arsenal head to Craven Cottage on Saturday.
Parker spent two seasons at Arsenal's bitter rivals Tottenham, clocking up 50 Premier League appearances.
Fulham marks the fifth London club that Parker has represented following spells at Charlton Athletic, Chelsea, West Ham and Tottenham.
