The BBC station had held the poll of sports fans in conjunction with the Commission for Architecture and the Built Environment.
And Sweeney presented his breakfast sports news from the winning venue on Friday.
The Glasgow ground that Celtic fans call Paradise took an amazing 60% of the votes, easily out-polling the Millennium Stadium in Cardiff and Lord's cricket ground in London.
Celtic and Nothern Ireland midfielder Neil Lennon was on hand to give Sweeney a personal view of his beloved club's ground - both as a fan and a player.
Even before donning the famous green and white hoops, he had already fallen in love with Celtic Park after coming across on the boat from Northern Ireland to watch the matches there from the age of 12.
"Particularly on European nights, it is a fantastic experience," said the 31-year-old who previously experienced England's top grounds while playing with Leicester City.
"My first Champions League game last season was against Porto and, when they lifted up the Champions League flag, the noise was just something else.
"The hairs on the back of my neck were standing up.
"60,000 people singing and lifting their scarves up. I just thought ' this is surreal'."
He also acknowledged the special emotions created by games between Celtic and often bitter Glasgow rivals Rangers.
"The atmosphere is just pure, raw aggression and just something I had never experienced before," said Lennon.
He confirmed that the stadium helped raise the team's performance.
"We were unbeaten in the Champions League at home last season and also beat Valencia here in the Uefa Cup on another great night," he said.
Fans were asked as part of the Radio Five Live poll to name what they liked best about their favourite sporting venue, from the design and facilities to the atmosphere on match days.
Celtic Park took 59.9% of the votes, 28.4% voted for the Millennium Stadium and 11.7% for Lord's.
A plaque has been presented to Celtic by CABE and Radio Five Live.
1. Celtic Park, Glasgow (Football)
2. Millennium Stadium, Cardiff (Football/ Rugby Union)
3. Lord's, London (Cricket)
4. Pride Park, Derby (Football)
5. Welford Road, Leicester (Rugby Union)
6. City of Manchester Stadium (Football/ Commonwealth Games)
7. Stadium of Light, Sunderland (Football)
8. St James' Park, Newcastle (Football)
9. Franklin's Gardens, Northampton (Rugby Union)
10. Brandywell, Derry (Football).