Multi-task learning remains a difficult yet important problem in machine learning. In Gaussian processes (GPs) the main challenge is the definition of valid kernels (covariance functions) able to capture the relationships between different tasks. This paper presents a novel methodology to construct valid multi-task covariance functions (Mercer kernels) for GPs allowing for a combination of kernels with different forms. The method is based on Fourier analysis and is general for arbitrary stationary covariance functions. Analytical solutions for cross covariance terms between popular forms are provided including Mat´ern, squared exponential and sparse covariance functions. Experiments are conducted with both artificial and real datasets demonstrating the benefits of the approach.