The Blades are struggling under the weight of £40million debts, with relegation into League One set to hit them even harder.
Trimming their wage bill was a priority this summer, and Henderson was among the high earners they were keen to move on.
The opportunity to link up with Millwall appealed to the striker and he has penned a two-year contract with the Lions.
He has taken a substantial pay cut in moving to The Den, but claims he was willing to do so in order to help the Blades in their hour of need.
"Last season was the worst of my career," said Henderson.
"I hold myself personally responsible for United's relegation because I didn't play enough games or score enough goals to help keep them up.
"I would have been happy to stay in Sheffield but, equally, I didn't want to be a drain on their finances."