Both roles are newly created positions after the business was bought from Premier Foods by Indian company Apeejay Surrendra Group last year for £80m.
Typhoo said that the new appointments were part of its promise to breathe new life into the brand.
Packer joins from Britvic where he headed the sales function for southern retailers. He started his career as a buyer for Sainsbury before moving into sales roles at Allied Bakeries and the consumer healthcare division of Pfizer.
Nall joins from Wilkinson Sword where he was marketing director. He has also worked for Anchor Foods and Young's.
The appointments follow the launch of a £5m campaign designed to revive the Typhoo brand. Packer said: "This new investment will allow the brand to play a more vibrant role in the category, which is in need of new ideas and fresh momentum."