Sharp, 29, who had a year left to run on his contract at Leeds, has joined the Blades for an undisclosed fee on a two-year deal with the option of another 12 months and returns to Bramall Lane for a third spell at his hometown club.
Sammon, 28, will spend next season with United on loan from Derby and both players could feature in coach Chris Morgan’s testimonial against Newcastle on Sunday.
“Delighted to get both players over the line and I’m looking forward to working with them,” Blades boss Nigel Adkins told the club’s official website.
“Billy is someone I know well and Conor is a player we have admired from afar and have monitored his progress since he was at Kilmarnock.”
The deal for Sharp ends speculation over his future which began in June when Adkins replaced Nigel Clough as Blades manager.
Sharp, who failed to nail down a regular place in Leeds’ starting line-up last season, has played under Adkins at three of his previous clubs – Scunthorpe, Southampton and Reading.
Leeds paid an undisclosed fee for Sharp in the summer of 2014 and in total he has scored 151 goals in 382 first-team appearances.
Sammon, who has nine caps for the Republic of Ireland, arrived in the UK when he signed for Kilmarnock in August 2008.
He had a spell at Wigan before moving on to Derby in a £1.2m deal in the summer of 2012 and has had previous loan spells at Ipswich and Rotherham.