Morrell, 24, has agreed a three-year contract, and Pompey have an option to extend the deal by a further year.
He only made 11 appearances for the Hatters after joining last October.
Midfielder Thompson joins after being released by Norwich City earlier this summer, and has signed a one-year deal with the option of another 12 months.
The 26-year-old, a former Wales Under-21 international, only registered 14 senior outings for the Canaries but he featured 21 times during a loan spell at MK Dons last season.
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