Slade was moved to head of football in Cardiff in May and replaced as manager by Paul Trollope.
The former Grimsby Town and Brighton boss left the Bluebirds on 3 June after just 28 days in his new role and was named Charlton boss three days later.
"That was my decision, I instigated that," said Slade, who joined Cardiff from Leyton Orient in October 2014.
Slade continued, "I believe in my own ability. I've been at Leyton Orient more recently for four and a half years.
"[I had] a couple of seasons at Cardiff but it was a mutual decision for me to leave and come to Charlton."
Slade has agreed a three-year deal at The Valley and is the club's sixth manager since March 2014.
Charlton were relegated to League One after finishing third-from-bottom in the Championship in 2015-16 and nine points adrift of safety, ending a four year spell in the second tier.
"I thought it was a good opportunity," Slade added. "The club maybe has lost its way, certainly last season.
"But it's an opportunity for me to get this club back on its feet and going in the right direction."
Russell Slade says he "instigated" his departure from Cardiff City to become manager of Charlton.