The 40-year-old former Dutch international, an assistant to Netherlands coach Bert van Marwijk, took charge of Ajax on a temporary basis last month.
De Boer started his playing career at left-back but later became a central defender and enjoyed distiguished spells at Barcelona, Galatasaray and Rangers.
He worked as a coach at Ajax's youth academy since 2006.
"I'm not surprised by this appointment as the intention of both sides was there from the start and we only needed to work out some details and that happened today," De Boer said on the club's official website.
Ajax director Rick van der Boog said De Boer had been their main candidate to succeed Jol.
"Frank (de Boer) knows the club as player and youth coach and knows exactly what is demanded and he knows what is going on in our youth department and which players are developing."
Ajax, fourth in the Dutch league six points behind leaders PSV Eindhoven with a game in hand, have won all three matches (Champions League, League and Cup) with De Boer in charge.
Ajax finished third in their Champions League group and have dropped into the second-tier Europa League where they face Anderlecht over two legs in the last 32 next month.
