The 21-year-old will spend the season at Elland Road after joining from Brighton & Hove Albion.
White, who stayed behind in England as United flew out to Australia to work on his fitness and get used to Marcelo Bielsa’s methods, impressed in Wednesday night’s 5-1 friendly victory over Tadcaster Albion.
With Jansson having been sold to Brentford earlier this month for around £5.5m, there is a vacancy alongside captain Liam Cooper in the back four.
Asked if he can replace the Swedish international, White replied: “Yes, I think so. I think I have got it in me to do it so we will see.”
White, who has had previous spells out on loan at Peterborough United and Newport County, admits taking part in the double sessions advocated by Bielsa and then sleeping in between has been “different”.
But the Poole-born defender is happy to be in West Yorkshire. “I had a couple of clubs that wanted to take me but Leeds seemed the most interested,” he said.
“We had a meeting in the summer and we discussed what I was looking to do this season and it fitted with my aims. That is why I came here.”
Meanwhile, Samuel Saiz has completed a permanent switch to Spanish club Girona in a deal understood to be worth around £2.5m.
The 28-year-old playmaker made 58 appearances in 18 months at Elland Road before forcing through a loan switch to La Liga side Getafe last January due to being homesick.
Hadi Sacko has also left Leeds for Turkish club Denizlispor. He joined United in 2016, initially on loan.