Pulis was confirmed as Alan Irvine's successor at The Hawthorns on New Year's Day and removed Rob Kelly, Keith Downing and Dean Kiely from the club's backroom staff on Monday.
Kemp arrives having worked with Pulis at Portsmouth, Plymouth Argyle, Stoke City and Crystal Palace, while Jewell has not occupied a managerial post since leaving Ipswich Town in 2012.
"I don't know what I've done to suffer Kempy again but I suppose I will have to put up with him," joked Pulis. "But the truth is that we have a working relationship which I value very highly – he knows what I want without even having to ask these days.
"Jewelly is someone I have known for a long time. We got to know each other on coaching courses as well as in opposition – he has massive experience and when I thought about what I wanted for this post, he fitted the bill perfectly.
"I'm delighted we have got him and I am sure the players will enjoy working with him.
"There are one or two other things we shall be putting in place over the next few days before everything is settled.
"It is never a pleasant task making changes because it always means some fellow professionals have to leave the club.
"I would just like to say that, while I only worked with Keith, Dean and Rob for a short time, they impressed me as top lads who I wish well for the future."
Pulis' reign started with a 7-0 FA Cup victory over Gateshead on Saturday and West Brom welcome Hull City to The Hawthorns this weekend.
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