They used a computer programme to analyse word patterns to pinpoint underlying emotions and work out their relative happiness.
According to the study, the basketball player came out top, followed by cyclist Lance Armstrong and television presenter Jonathan Ross.
These were closely followed by comedian John Cleese, while tennis player Andy Murray and comedian Russell Brand were equal in fifth place. Rapper Snoop Dogg was the least happy.
Politicians followed in the study - Al Gore, Arnold Schwarzenegger and Barack Obama - tended to show emotion on single topics, such as climate change or healthcare, the study found.
Britney Spears, Philip Schofield and Boris Johnson were also included in the research.
The team also found the majority of tweets by celebrities were happy and positive, especially when they talked about forthcoming events or other celebrities.
The researchers now plan to use the technology to analyse the links between emotion and important lifestyle issues. They want to identify whether widespread social problems - such as obesity and alcoholism - have common emotional links that could be detected by following people's online communications.
The study focused on tweets made by celebrities because they tended to put more emotional content into their tweets and because the information was more easily available.
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