Besta, 27, was handed a game in Wednesday's 4-1 win over a Newcastle XI and joins the Keniloworth Road club having represented the Czech Republic seven times at Under-21 level. He joins after a season in Slovakia with Ruzomberok.
He also arrives with European experience following seven years at hometown side Banik Ostrava, where he won the Czech league title in 2004, played in the Champions League qualifying rounds and made a UEFA Cup appearance against Middlesbrough.
Kroa impressed in Town wins over Kilmarnock and Newcastle, scoring the winner against the Scots and then signing on the same day as the victory against the Magpies. The 29-year-old defender, has 169 league appearances under his belt in ten years with hometown club Tescoma Zlín.
Luton manager Richard Money, said: "Make no mistake these are two players of the highest calibre. We are extremely lucky to have them.
"Having Zdenk and Pavel in our squad boosts our chances of a successful season. Why? Because they are players who should be playing at a higher level.
"Besta is tough, uncompromising, a proper central midfielder player while Zdenek brings a calmness to the back four which will enable us to build well from the back.
"I am thrilled to welcome them both to the club and cannot wait for them to show the Blue Square Bet Premier what they're all about.
"It also shows how well regarded this football club is across the globe. Everyone is of the opinion that this club should be playing league football, that's a view shared Zdenk and Pavel."