Context. The advent of the Fermi gamma-ray space telescope with its superb sensitivity, energy range, and unprecedented capability to monitor the entire 4π sky within less than 2–3 h, introduced a new standard in time domain gamma-ray astronomy. Among several breakthroughs, Fermi has – for the first time – made it possible to investigate, with high cadence, the variability of the broadband spectral energy distribution (SED), especially for active galactic nuclei (AGN). This is necessary for understanding the emission and variability mechanisms in such systems. To explore this new avenue of extragalactic physics the Fermi-GST AGN Multi-frequency Monitoring Alliance (F-GAMMA) programme undertook the task of conducting nearly monthly, broadband radio monitoring of selected blazars, which is the dominant population of the extragalactic gamma-ray sky, from January 2007 to January 2015. In this work we release all the multi-frequency light curves from 2.64 to 43 GHz and first order derivative data products after all necessary post-measurement corrections and quality checks. Aims. Along with the demanding task to provide the radio part of the broadband SED in monthly intervals, the F-GAMMA programme was also driven by a series of well-defined fundamental questions immediately relevant to blazar physics. On the basis of the monthly sampled radio SEDs, the F-GAMMA aimed at quantifying and understanding the possible multiband correlation and multi-frequency radio variability, spectral evolution and the associated emission, absorption and variability mechanisms. The location of the gamma-ray production site and the correspondence of structural evolution to radio variability have been among the fundamental aims of the programme. Finally, the programme sought to explore the characteristics and dynamics of the multi-frequency radio linear and circular polarisation. Methods. The F-GAMMA ran two main and tightly coordinated observing programmes. The Effelsberg 100 m telescope programme monitoring 2.64, 4.85, 8.35, 10.45, 14.6, 23.05, 32, and 43 GHz, and the IRAM 30 m telescope programme observing at 86.2, 142.3, and 228.9 GHz. The nominal cadence was one month for a total of roughly 60 blazars and targets of opportunity. In a less regular manner the F-GAMMA programme also ran an occasional monitoring with the APEX 12 m telescope at 345 GHz. We only present the Effelsberg dataset in this paper. The higher frequencies data are released elsewhere. Results. The current release includes 155 sources that have been observed at least once by the F-GAMMA programme. That is, the initial sample, the revised sample after the first Fermi release, targets of opportunity, and sources observed in collaboration with a monitoring programme following up on Planck satellite observations. For all these sources we release all the quality-checked Effelsberg multi-frequency light curves. The suite of post-measurement corrections and flagging and a thorough system diagnostic study and error analysis is discussed as an assessment of the data reliability. We also release data products such as flux density moments and spectral indices. The effective cadence after the quality flagging is around one radio SED every 1.3 months. The coherence of each radio SED is around 40 min. Conclusions. The released dataset includes more than 3 × 10⁴ measurements for some 155 sources over a broad range of frequencies from 2.64 GHz to 43 GHz obtained between 2007 and 2015. The median fractional error at the lowest frequencies (2.64–10.45 GHz) is below 2%. At the highest frequencies (14.6–43 GHz) with limiting factor of the atmospheric conditions, the errors range from 3% to 9%, respectively.