Jol's grip on his position as boss at White Hart Lane has looked fragile since reports in Spain of a meeting between Spurs officials and Sevilla boss Juande Ramos, compounding the club's poor opening week of the Premier League.
Levy admitted in a statement that the board "constantly assess our position and performance", and underlined his determination to finish in the top four following his meeting with Jol.
The support for the Dutchman from his chairman suggests Jol could be given this season to deliver.
"I am an ambitious chairman, we are an ambitious club and we want Champions League football at White Hart Lane.
"We, the board, owe it to the club and the supporters to constantly assess our position and performance and to ensure that we have the ability to operate and compete at that level.
"We have made a massive investment in the squad and as a result we have the best squad of players this club has had for over 20 years and they are equally hungry for success and silverware.
"For that we need our management and coaching standards to be of the highest quality such that players can fulfil their potential and we can compete with the best.
"We have discussed all of these expectations with Martin and he has confirmed to me today that he feels he is equipped with a squad and a determination to take on that challenge."
Jol admits there is now pressure on him to deliver Champions League football after spending around £40million in the summer.
He said: "We had a full and frank conversation and I fully understand the ambitions of the club - they are the same as those of the supporters.
"He has put a lot of hard work into this club and with the squad of players we have assembled, it is realistic that we should look to challenge for a top-four position and I have assured him and the board that is what I shall aim for.
"The last two seasons we have finished fifth and this season we start with an even better team. So we should be optimistic.
"Yes, it is pressure to deliver, but that is what we managers should expect. Hopefully all the media will relax now - all I shall be concentrating on is each and every game."