Owner Ann Budge revealed that Neilson was invited to attend the meeting and got total support from the directors. Despite criticism from a section of the club's support due to recent results, Budge said Neilson will be given the chance to strengthen his squad during the January transfer window.
Hearts had managed just three points from their last four matches in the Ladbrokes Premiership before Saturday's home game with Motherwell.
Budge also stated that the club's target for this season has to be at least third place having finished there last season and qualified for Europe.
"We had a board meeting yesterday and I invited Robbie along to talk about where we are. The whole board is very happy with what we're planning to do and Robbie knows he has the backing of the whole board," said Budge, talking to BBC Sportsound.
Asked if Neilson will get resources to improve his team, Budge replied: "Yes. We all spoke to Robbie. He is happy. He left the board meeting happy knowing he is going to get what he needs to help us achieve what we want to achieve.
"We finished third last season so my view is anything less than third is not very good. If we qualify for Europe and finish in the top three or four, that would be fantastic. It's very tight and it has been all the way through. Each team has had chances to get ahead.
"The next couple of months will be fairly crucial. We have two games against Rangers and they're big games. We keep going and focus on what we're doing. Others focus on what they want to do."
Budge added that she could remain in place at Tynecastle for many years to come. The club are currently building a new £12m main stand and she said she has no intention of going anywhere soon despite being in her late 60s.
"I can see myself being here for a while. One of the supporters asked me what they have to do to tie me to this place for ten or 15 years, but I think I'm managing to do that myself."