Former Doncaster, Oldham and Bristol Rovers boss Penney takes the role of assistant manager from Graham Coughlan, who in turn becomes first-team coach, while Shaw arrives as head of recruitment and scouting.
Shrimpers manager Phil Brown told the club's official website: "I'm thrilled that Dave has joined the club and I'm sure the whole team will benefit from having him around.
"He has an excellent understanding of this level having won promotion with Doncaster back in 2003/04.
"Bob will have to hit the ground running as we prepare for the new season, it will all move very quickly now in terms of identifying players who he feels can come in and do a good job for us."
Brown added: "I'm delighted to have kept Graham here. His passion and knowledge was first class last season and he was a huge help to me after I was appointed manager. He works extremely hard and is very good at getting the best out of players, he will have an important role to play throughout the season."
Meanwhile, Seedy Njie and Ryan Augur have both penned one-year professional contracts with Southend.
Striker Njie rose through the ranks to make his first-team debut as a substitute in last season's Capital One Cup defeat at Peterborough before again stepping off the bench in the final game of the campaign against Morecambe.
Right-back Augur, 19, has been at the club since the age of 11 although he is yet to make his first-team debut.
The news comes after winger Mitchell Pinnock, another Academy product, signed his first pro deal with the League Two club last month.