Bremen have won four Bundesliga titles, most recently in 2004, and six German Cups, the last in 2009.
Schalke have won the German league seven times, the most recent in 1958, and are five-time German Cup winners, last lifting the trophy in 2011.
"Pre-season is over and now it's time to deliver," Schalke's new coach Frank Kramer warned ahead of their opening fixture against Cologne on Sunday.
Bremen open at home against Wolfsburg today with champions Bayern Munich kicked off the campaign against Europa League winners Eintracht Frankfurt.
While Schalke and Bremen only had to wait one season to return, they have adopted contrasting approaches as they seek to stay at the top table.
Schalke have brought in a dozen new players to the squad which won the second division title while Bremen have opted to stick with the core of the side that won automatic promotion with second place.