Meulensteen's arrival after the 4-0 Barclays Premier League defeat at Liverpool two weeks ago was thought to have increased the pressure on Jol with the former Anzhi Makhachkala boss viewed as the club's manager in waiting.
Fulham are third from bottom in the table and have lost their last four matches in all competitions with Swansea visiting Craven Cottage on Saturday.
But Jol has revealed that it was his decision to recruit Meulensteen, who left Manchester United's coaching team in the summer before a brief spell at Anzhi, in an attempt to ignite their ascent up the Premier League.
"I'm really pleased he's here. I thought he was making a choice to go elsewhere - first to Germany and then Qatar," Jol said.
"It was maybe by coincidence that I texted him again and he said that he'd come back to England.
"We needed something, more rhythm. We weren't playing with rhythm and we needed more energy.
"I thought we needed something and he's the right guy. But now we need the results. There's a new spirit and a good spirit."
Fulham face Swansea without centre-back Brede Hangeland who continues to nurse a sciatic nerve problem with Jol unable to set a date for his return.
"It's a real problem with Brede and he won't be involved. Each week I thought he'd come back but he hasn't," Jol said.
Jol admires Swansea's progress since their entrance into the Premier League in 2011 but points out that Fulham have produced superior results during the same period.
"The Liverpool defeat was two weeks ago. There's a new game coming up and we want to do better," he said.
"Swansea play in a very good way that is probably the way we'd like to play.
"Over the last couple of years Swansea have done extremely well, but over the same period we have more points than them.
"That's very positive and people don't notice it, but it's true. We're ready for this match."
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- Barclays Premier League
- Anzhi Makhachkala