Allan, who has been at St Modwen for almost three years, will take up the new role no later than 1 June next year.
FTSE 100-listed LandSec announced the departure of Noel in the summer, when he said it was “the right time” to move on, having secured “a growing pipeline and a clear strategy for the future”.
It recently revealed a swing to a £147mln loss before tax for the first half because of a hole in the value of its assets.
“Mark has been a highly successful chief executive of two companies in the property sector,” said chair Cressida Hogg in a release.
“He has demonstrated strong management skills and the strategic insights that we believe will build on the strengths of our business today and be invaluable for the next phase of Landsec's evolution.”