Bresnan missed the second Test against Bangladesh with a foot injury, while Bell hasn’t played a one-day international since 2008.
Andrew Strauss returns to captain the one-day squad, and bowler James Anderson is also named after both were rested for the tour of Bangladesh in March, the England and Wales Cricket Board said in a release.
Sussex all-rounder Yardy is selected in a 13-man squad that includes 11 players who helped England win the ICC World Twenty20 tournament in the West Indies. Craig Kieswetter is picked as wicketkeeper-batsman rather than Matt Prior.
“The challenge facing the squad now is to maintain the form they showed over the winter against the world’s No. 1 side in 50-over cricket,” national selector Geoff Miller said.
England plays five ODIs against Australia, starting at Southampton on June 22. The Scotland match is in Edinburgh on June 19.
England squad: A.J. Strauss (capt., Middlesex), J.M. Anderson (Lancashire), T.T. Bresnan (Yorkshire), I.R. Bell (Warwickshire), S.C.J. Broad (Nottinghamshire), P.D. Collingwood (Durham), C. Kieswetter (Somerset), E.J.G. Morgan (Middlesex), K.P. Pietersen (Hampshire), R.J. Sidebottom (Nottinghamshire), G.P. Swann (Nottinghamshire), L.J. Wright (Sussex), M.H. Yardy (Sussex).