There are already a lot of infirmations in forum discussions.
Search for "F V converter".
There are ready to buy ICs. Each of them come with a datasheet. The datasheet should be sufficient to build the circuit and calculate the part values. You may find additional informations at the manufacturer's internet pages in application notes and other documents.
The capacitors require to be very stable, and the National Semiconductor (now Texas Instruments) CLEARLY indicates that they have to plastic film types. Read the whole datasheet.
Unfortunately your frequency shown in the oscilloscope waveform is very low (7.25 Hz). This means two drawbacks: very large film capacitors and a very long settling time and/or large ripple voltage.