Johnson, a Fox analyst, won two Super Bowls with the Cowboys and built the bulk of the roster that won a third title for the team after his departure.
He was clearly emotional upon receiving the news Sunday, as was his former quarterback Troy Aikman, who could be seen tearing up as he heard the announcement from Green Bay, where he was announcing the playoff game.
"The only thing I can think of is all of the assistant coaches that worked for me, all the great players that played for me, they're the reason I'm here,'' a choked-up Johnson said after Baker told him he was a Hall of Famer. "I can't talk. This is so special.''
The Hall's centennial class was selected by a blue-ribbon panel this past week, and the remainder of the 15-member class will be revealed Wednesday. Baker announced Saturday that former Steelers coach Bill Cowher also would be enshrined as part of the centennial class.
When fully revealed, the centennial class will include 10 seniors candidates, as well as three contributors to go with Cowher and Johnson. The class was chosen as part of the NFL's 100th anniversary.
The panel -- which included members of the Hall's board of selectors, league historians, Hall of Famers, as well as New England Patriots coach Bill Belichick -- chose the class from a list of 38 finalists during a meeting at the Hall of Fame on Wednesday.
The 38 finalists were chosen from a list of almost 300 nominees over the course of the past five months.
The Hall of Fame's Class of 2020 -- composed of modern-era players -- will be selected Feb. 1 in Miami Beach, Florida, the day before Super Bowl LIV.
The Cowboys went 1-15 in Johnson's first season as coach in 1989 but steadily improved until the team won back-to-back Super Bowls in his fourth and fifth years. The Cowboys went 36-12 in Johnson's last three seasons in Dallas, winning two Super Bowls.
Johnson and Cowboys owner Jerry Jones clashed following the 1993 season, and Barry Switzer directed Dallas to a Super Bowl win to close out the 1995 season with a roster largely assembled by Johnson.
"We're so happy that the Hall of Fame has recognized Jimmy Johnson for what he is: a great coach," Jones said in a statement Sunday. To Jimmy I say, 'The stars were aligned and our dreams came true when we joined the Dallas Cowboys.' And on behalf of the Cowboys, and our fans all over the world, I say congratulations Jimmy. We're proud of you."
Johnson's work not only as a coach, but as a personnel evaluator, was cited in his case for Canton. He is often credited for the draft chart that used a point value for each draft pick to determine what selections should be used in trades.
Every team uses some version of the chart in its draft preparations. In his most notable trade for the Cowboys, Johnson dealt running back Herschel Walker and quarterback Steve Walsh after his arrival, and those trades netted him four first-round picks, four second-rounders and two third-rounders.
"Jimmy was the only coach on planet earth that could control the amount of alpha dogs he had on those Super Bowl championship teams," Ring of Honor safety Darren Woodson. "He had a way of pushing all the right buttons to motivate his team. I'm honored to have been drafted by Jimmy. I'm so happy for him to achieve this rightful honor for what he did for our team."
Overall with Dallas, he drafted 18 players who went on to start in Super Bowls, 15 players who were named to the Pro Bowl and three players who eventually were named Super Bowl MVPs. In his four-year tenure with the Dolphins, he drafted four players who went on to a combined 19 Pro Bowls (Zach Thomas, Jason Taylor, Sam Madison and Patrick Surtain), and none of the four was a first-round pick.