The smiling Australian is one of Formula One's fan favourites and his arrival last year at McLaren, the former home of greats like Ayrton Senna and Lewis Hamilton, had promised much.
Brown said the eight-times grand prix winner, who led a one-two finish at Monza in Italy last season, had brought a lot of energy to the team and his positive outlook would be missed.
"Daniel's a wonderful person, and a great person to be around. We've had many laughs and we've sprayed champagne together. It's very personal," added the American.
"Today is a sad day that things didn't work out as we'd hoped they would.
"I'm going to look back with some very fond memories, some fun times together on and off the track. We're in a business...we need to focus on ultimate performance and we wish Daniel the best.
"There's absolutely no ill will between us. It's all very amicable and I think he too has had a very good time at McLaren."
Ricciardo joined from Renault as a proven race winner but struggled to match the performance of British team mate Lando Norris, a rising star popular within the team and on a long-term contract.
The Australian never felt fully comfortable in the car despite all his experience, especially in trying to push it to the limit.
Asked about a possible backlash from fans after the team discarded the driver with a year to run on his contract, principal Andreas Seidl emphasised the effort put in to make things work.
"We tried everything we could from both sides. Unfortunately we couldn't make it work which is obviously also my responsibility," he said.
Brown said discussions with Ricciardo had been going on throughout the season and the team had been very transparent.
"He's been around motor racing his entire life so he understands and is as disappointed as we are that it didn't work out," he said.
"He gets it and we hope he lands in a good race car next year and we see Daniel back to the form that we know he's very capable of."
