The 34-year-old keeper has taken a £750k drop in salary so he can resurrect his career with The Whites.
The former Scotland keeper swapped Stamford Bridge for Elland Road yesterday, despite having a year left on his £20k-a-week Chelsea deal.
Sullivan agreed to join Leeds on a two-year contract worth a reported £5k a week.
Blackwell said in the Yorkshire Post: "Neil never discussed money at all, he just accepted what we offered him. All he wants to do is get playing football again, that's the most important thing for him. We may not be in the Premiership this season, but he couldn't be getting the opportunity for first-team football with a much bigger club than Leeds United.
"The key for him was football, not finance and I'm delighted to have got a keeper of his experience and ability because apart from anything else he can be a big influence on Scott Carson's development.
"Scott is only a kid with a lot of things still to learn and he couldn't have a better teacher than someone with Neil's pedigree. Sully is a good talker and organiser and this is the chance for him to kick-start his career."