Bywater, 35, started the final three matches of last season after injury to Jon McLaughlin, who was later released.
The former West Ham and Derby keeper has signed a 12-month contract extension at the Pirelli Stadium.
Ex-Watford forward Sordell, 26, scored four goals after joining Burton from Coventry in January and has agreed a new three-year deal.
Bywater joined West Ham as a 16-year-old in February 1998, from Rochdale's youth ranks, and featured in their 1999 FA Youth Cup-winning team alongside Joe Cole and Michael Carrick.
He spent eight years at Upton Park before signing for Derby in 2006 and later had spells at Sheffield Wednesday, Millwall and Doncaster, among others.
"He's proved his worth in the last part of the season. Next season he might not be back-up," manager Nigel Clough told the Brewers' official website.
Experienced goalkeeper Stephen Bywater and striker Marvin Sordell have agreed new contracts with Burton Albion.