Land Securities, which owns the Bluewater shopping centre in southeast England, said Allan will take over from Noel no later than June 1 and will receive an annual salary of 800,000 pounds ($1.03 million).
"Mark has been a highly successful CEO of two companies in the property sector. He has demonstrated strong management skills and the strategic insights that we believe will ... be invaluable for the next phase of Landsec's evolution," Chairman Cressida Hogg said.
St. Modwen separately said it had begun looking for a successor to Allan.
Allan was also the former chief executive officer of Unite Group.
Jefferies analysts said both St. Modwen and Unite grew under Allan, with St. Modwen's share price appreciating 64%.
For Land Securities, the announcement comes just 10 days after it posted a loss for the first half, as UK store closures took a toll.
Noel's departure date has not been decided, Land Securities said. He joined the FTSE 100 company as managing director of its London portfolio in 2010 and became the CEO in 2012.
(Reporting by Pushkala Aripaka in Bengaluru; Editing by Shailesh Kuber, Bernard Orr)