Hellickson and Walker were the only two of the 10 players extended qualifying offers this offseason to accept them.
Among those who did not accept their qualifying offers were New York Mets outfielder Yoenis Cespedes, Toronto Blue Jays designated hitter/first baseman Edwin Encarnacion and right fielder Jose Bautista, Baltimore Orioles designated hitter Mark Trumbo, Chicago Cubs center fielder Dexter Fowler, Los Angeles Dodgers third baseman Justin Turner and relief pitcher Kenley Jansen, and Texas Rangers shortstop/outfielder Ian Desmond.
All eight of those players will remain free agents, but any team that signs them must surrender their first-round draft pick (top 10 protected) to the player's former team.
Monday was the deadline for players to accept or reject the offers.
Hellickson, the former American League Rookie of the Year in 2011, is entering his second season with the Phillies and eighth in the majors. In 2016, Hellickson was 12-10 with a 3.71 ERA and a career-high 154 strikeouts in 32 starts.
Hellickson spent his first five big league seasons with the Tampa Bay Rays, going 40-36 with a 3.78 ERA in 115 games (108 starts), before being traded to the Arizona Diamondbacks on Nov. 14, 2014. He was then traded to Philadelphia exactly one year later.
Hellickson won a Gold Glove Award during the 2012 season with Tampa Bay.
Walker, 31, hit .282 with 23 home runs and 55 RBIs in 113 games with the Mets in 2016. The longtime staple of the Pittsburgh Pirates' infield and 2014 Silver Slugger Award winner was traded by Pittsburgh to New York for Jon Niese on Dec. 9, 2015.