Twigg set up LightBrigade in 2011 after he left what was then Fishburn Hedges' consumer arm, 77 PR, where he was managing director for five years.
Twigg was previously managing director of Nexus Communications.
Way to Blue has offices in London, Paris, Sydney, Los Angeles, Amsterdam, Munich, Rome and Madrid, and works across film, home entertainment, television and consumer brands.
Current clients include Universal Pictures, 20th Century Fox, Amazon Prime, IMAX, Mattel and Red Bull.
Twigg said: "I looked at a number of potential agency options and Way to Blue is quite simply a really impressive group of talented people experiencing significant growth with innovative work and rammed with lots of hunger and ambition. Our skills and our outlook on life complement each other beautifully and we are confident of continuing to build and deliver a truly integrated offer."
Way to Blue CEO Adam Rubins added: "We have been growing our consumer brand work for some time and Alan will help us accelerate that growth. He brings a wealth of experience to our PR offer and his track record in working with big brands and creating award-winning campaigns is formidable."