Beltrami fields $\mathbf{F}$ are complex vector fields which satisfy the equation $\operatorname{rot}\mathbf{F}+ \lambda \mathbf{F}=0$. Such fields appear in many branches of physics like astrophysics, electromagnetic and plasma physics. In this work we will show how to construct Beltrami fields using transmutation operators, giving a complete system of solutions for the case when $\lambda$ depends only on a single variable. Moreover if $\lambda$ is a complex constant, using the proyectors $\mathcal{P}^\pm=M^{\frac{1\pm \mathbf{ie}_3}{2}}$, we have the following representation \begin{align} \mathbf{F} = \sum_{n=0}^\infty \; \sum_{l+m=n}\big( \mathcal{P}^+\mathbf{T}_f[{P}^{l,m}] +\mathcal{P}^-\mathbf{T}_{1/f}[{P}^{l,m}] \big)\vec{c}_{l,m}, \end{align} where the purely vectorial quaternionic constants $\vec{c}_{l,m}$ are \[\vec{c}_{l,m}=\frac{1}{n!} \frac{\partial^n \mathbf{F} (0)}{\partial_1^l\partial_2^m}\] where $n=l+m$ and these series converge uniformly in every $B_{R'}(0)\subset B_{R}(0).$