Will a 42RLE or AW4 automatic transmission swap to my 1999 TJ?

A 42RLE wouldn't work at all due to all the electronics it needs. An AW4 would work but it runs hotter and isn't an easy installation. I'd go (and did) for the 32RH automatic transmission which is a bolt-in transmission. I converted my '97 from its OE 5-speed manual to the 32RH probably 15 years ago and got it done in a weekend. The 32RH is what came in the TJ until 2003 so it was made for your '98. You just need to swap in a different PCM programmed for the automatic and your '98 model year, the wiring is already in place. You just need the mounting hardware, transmission cooling lines, mounting hardware, flex plate, and a radiator made for an automatic if yours isn't. It's ready for an automatic if it has a couple ports on the bottom.

The 32RH recommendation assumes you have the 4.0L engine. If you have the 2.5L engine, that recommendation becomes the 30RH.
 
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What is the major modification that i need to do to put a AW4 transmission in my TJ? Have a 98 XJ parts jeep. Its all complete. So have the computer also.