The singer-songwriter was interviewed by Fearne Cotton for the programme and also took to the stage to perform his biggest hits, including Stay With Me, Too Good at Goodbyes and Writing’s on the Wall.
One of the most emotional moments of the broadcast was Smith’s unexpected appearance at the wedding of Lisa and Bec.
Smith, 25, surprised the newly-weds at their reception and performed a moving rendition of his ballad Latch, and later told Cotton it was the first LGBT wedding he had attended.
It proved to be too much for some fans, with one writing on Twitter: “Highlight of my night was definitely crying watching a wedding of 2 people I don’t know.”
Another said: “The wedding was so cute I’m actually crying.”
“Sat here crying at Sam Smith surprising a couple at their wedding. I’m such a soppy cow at times,” one said.
For other viewers, the combination of Smith’s emotional songs and his voice prompted weepiness.
“@samsmithworld I think I just spent the whole of “Sam Smith at the BBC” singing my heart out and almost crying at every song!” one fan wrote.
One said: “Sat with me dad listening to Sam Smith singing Stay With Me and crying. Can my eyes behave themselves now please?!
One viewer said they were “crying like a baby” throughout the episode while another said they needed to “get a grip”.
They added: “His voice, the words. It’s just making me cry.”
“@samsmithworld we’ve all just sat watching you #SamSmithAtTheBBC and not a dry eye in the house!” one fan said.
“Truly amazing talent… #inspirational.”
Smith, who is known for his emotional songs that are often based on heartbreak, told Cotton he is “really happy for once”.
He added: “I’ve always been happy, I just know how to focus my sadness.”
Smith’s second album The Thrill of it All was released last week.