Yes, he is taking the helm at Chelsea from now on. It was an unexpected kind of move for most people as far as I can see. Because Chelsea has been mostly going for coaches with an impressive career.
We have seen big names managing this team very often. But in the recent years they also joined the current trend. They want to try different coaches than the usual. They tried Potter and Lampard but they couldn't get the result they expected. After Pochettino they want to rejoin this trend. However Boehly should know that it is better to be patient to get results. The first season might not be great, everyone isn't Xabi Alonso.
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Pochettino was a fairly good coach only that he needed more time to build that understanding he required from the management team and probably since he left the PSG, and returned back to the Premier League again. I also feel he's a big coach and a lot of people expected big results from him but his performance with Chelsea can be rated average or a bit below for someone has been as him. His performance and that of Eric Ten Hag is not far-fetched from each other.
Now that Chelsea have decided to part ways with him, he should just take a break and restrategize. What I've understood with most of these managers especially for Pochettino is, whilst he's a celebrated manager of his own rights, he would still go on to have issues with his management teams like he had with Paul Winstanly and Lawrence Stewart who are both two sporting and recruitment directors employed by the team owner to give support. All these little disagreements are nothing but distractions to some of these professional managers.